Komposisi Fungsi Part 1 - Operasi Aljabar Pada Fungsi [ Matematika Wajib Kelas X ]

Hi assalamualaikum warohmatullohi

wabarokatuh meet me again with Deni

Handayani on the metlife channel in

this video we will learn the material of

function composition and this is the first part of the video

there are three sub materials that

we will learn in this first part of the video

including the first

algebraic operations on functions including addition subtraction

multiplication and

division operations Sumatra second we will

learn about the properties of

algebraic operations on functions and Sumatra

third we will learn how to

determine the domain of the results of algebraic operations of

several functions Okay a person

Let's just discuss the material

clap

[Music]

Okay now we will learn the material of

algebraic operations on functions actually

this is the material that friends have

learned in grade 8 of junior high school but consider

this to refresh your memory because

we will use this material in the

next Sumatra Okay Let's just discuss

for example there are two functions including

function f and function G then the

following algebraic properties apply

first for addition if

friends find a form like this

F + GX that means it is the same as f x

plus GX Then for subtraction F

Min GX it is the same as f x minus

GX likewise for multiplication F * GX

is = FX * GX see the writing and

also with the division F divided by GX

is the same as fx divided by GX no for

division there are conditions yes remember for

division it cannot be divided by

zero while here the gps is

as a divisor then GX is not Hi can be

zero so that this is defined

because we discuss the example of the problem for

example given three functions fx GX and

hx like this yes we will find the

first F plus GX then F minus

GX then the third G * hx and the

4th G divided by kxk we Answer the first

First for F plus GX this is the same

as fx plus GX friends

pay attention to the fx function the fx function is 3

x to the power of 3 min 2 x squared + 4 X min 5

so the effect we replace with this

friends so 3x to the power of 3 min 2 x

squared plus four X min 5 then

add GX pay attention to the GX GX function this one is

x squared min 5 x + 6 we

write x squared min 5 x plus six

next friends

just add it up Hi and remember to

add algebraic forms friends

can only add the

same powers that are the same degree Here the

cube power is no longer there so the

cube power we rewrite

then the ^ 2x squared here

there are two namely min 2 x squared and x

squared we add see the

coefficient is this coefficient is

negative two here positive 1 min 2 plus

one that is bin1 so here min 1x

squared or written min x squared

then the variable x here there are two

namely 4x and mi5x directly so

add 4 plus negative 5/4

minus 5 how much is negative 1 Bro so

negative 1x or negative X then

the constant or the number is negative 5 and 6

mi5 + 6 how much is positive one so plus 1

well this is the result of the addition is

easy right friends can only

add terms that are the

same degree or the same power

then for subtraction number 2f

minus GX is the same as f x

minus GX the method is the same as FX which we

rewrite yes FX is this one 3x to

the power of 3 min 2 x squared 4 X min 5 we

rewrite then subtract it

as a note for subtraction

make sure friends Give brackets

different from addition not given

forums problem yes to subtract

make sure friends Give brackets

yeah minus GX GX that is x squared

min 5 x + 6 in brackets okay

now we open the brackets

here we rewrite then

this is negative times positive negative times Positive

that is negative so negative x

squared negative times negative it becomes

positive so here it becomes plus 5x negative

times positive negative now min 6 clear yes

Now we add the

same degree that has the same power

as before here the third power is no

longer there so we rewrite 3x ^ 3

which is SWT here where min 2 x squared

and this is min x squared negative 2

minus one negative 3 so negative 3

x squared then the X only 4x and 5x

4 x + 5 x9x then negative 5 minus

6 negative 11 and this is the result of

my subtraction so the difference for

addition friends is no problem

No Give brackets but for

subtraction make sure Give brackets

Okay now we discuss the third

multiplication for multiplication GK cleverly =

GX times hxd.exe it is x squared minus

5 x + 6 then times the right x minus

two Now the way to switch it friends

multiply one by one yes Hi x squared

multiply by snack and X ^ 1 if

multiplied by the power it is added JD x ^

2 * x ^ 1 means x to the power of 2 plus

one x ^ 3 remember the power is added

then x squared times negative duet

becomes negative 2 x squared then

this one

Min 5 x times x this is the power of -1 this ^ 1

batia Next becomes the power of 2 which is not

Min 5 x times x min 5 x power of 2

then Min 5 x * min 2 negative times

negative is positive so plus 10x

then this is six times x6x then six

times negative 2 negative

12 next we Simplify we

operate the same power here the

power of three is no longer there yes we

write again x ^ 3 which is the power of 2 here

there are two friends min 2 x squared

minus 5 mint container two minus

5 How much is min 7 so min 7 x squared

then the variable X here is 10 x

+ 6 x how much is 16x then minus 12

Okay now we discuss the fourth

division question y divided by hx this is the same

meaning as GX divided by hx GX is x

squared min 5 x + 6 and the result is

X min 2 Now for division if

this can be factored friends

factor it x squared min 5 x + 6

we factor it into X min 2 B min

3 Now for those who are still confused about how

to factor it I have

discussed the video later the link will be included

in the description of this video Eh how to

factor the quadratic form so if

I discuss it again here it seems

too long now friends pay

attention between the numerator and denominator

there are the same or not X min 2 B

min two we just cross it out so the answer

is a Hi min 3 with the note that the

divisor cannot be zero so hx

cannot be zero while

zekhan X min 2 X min 2 is not equal to

zero meaning X not equal to zero

plus 2x is not equal to two this is

the condition Well that's how to do

algebraic operations on functions including addition subtraction

multiplication and

division yes that simple now

we discuss eh next moment namely the

properties of algebraic operations on functions

there are four properties the first for

addition is commutative

meaning if friends find F

plus GS it can be reversed to g-plus

FX so for addition it is

commutative meaning the order can be

swapped okay Then the

second associative property in addition

well in addition besides commutative is

also associative for example there are

three

c & f plus getplus X that friends

can do efxplus Bank of Tokyo

can also g-plus first freely because this is

associative then the third besides addition multiplication is

also the same it

is commutative yes commutative property

in multiplication FK Lights the value will be the

same as gkfx so the order will be

reversed the result will be the same then

the fourth multiplication is also

associative FK liege times hx Friends

can do FKG first or can

also do GK see first the results will be the same

Well these are the properties of algebraic operations

on the function now we discuss the

last material in this video,

namely the domain of the function of the result of

algebraic operations of several functions first

for the domain of the result of the addition for example

friends will find the domain of the addition of

function f and function G the domain

of the result of the addition of F with G is the

intersection of function f with the domain of

function G so friends must be able to

find the domain of the function first eh

for example for example it is known that the function fx

= 3 x squared and the function gx is

the root of x + 5 Determine the domain of the domain

the domain is the same as the domain yes the

domain of the function f plus GX

first friends find the domain

of the function fx the function fx is 3 x squared

here are there any exceptions or not If x

squared it can invite nxc whatever it is, it doesn't

matter so the domain of the function f is all

real numbers X Bima X members of

real numbers Then for GX GX = root x + 5

Well for the roots there are conditions

friends the contents in the roots

cannot be negative yes so here the domain is

filled in so that it cannot be negative

meaning the contents in The root must be

more than or equal to zero so x +

5 is more than 10 then x is more than or

equal to zero minus 5 negative 5

then the domain of gfxdomain G is

x where x is more than = negative 5 and X is a

real number member well this is the domain

of the function G remember if the function

is a root then the domain inside the

root cannot be negative or must be

more than or equal to zero Well now

we look for the intersection friends we

make a number line so friends

can see the first illustration the

domain of f here is all X where x is a

real number member weight in all the

numbers on this number line

that is the domain of the function f Well

now the domain of the function g x is more than =

negative 5 negative helps which This

means from here more than that means

to the right Gan teh negative 5 to the right well the

intersection is the area that is shaded

by both make sure the area here

friends yet i come here then

the intersection domain of efxplus G is x

where x is more than = negative 5 and X is a

real number member

Okay now we continue How to

determine the domain of the subtraction result

for example there is a subtraction of the function f

minus G then the domain of the

subtraction result is a slice of the domain

F and the domain is not so the method is the same

we take the slice for example

if it is known that the function fx is three

over x + 2 and GX = root x minus three

Determine the origin of the region when

the domain of f minus GX the method is the same

we first find the domain of the effect function FX is

3 over x plus two Well if the

root form is the condition inside

so that it cannot be negative Well if

friends find a division or

rational form like this the condition is the

divisor or the one in Mbak or the

denominator must not be zero

Why because if it is divided by zero it is not

defined yes so here the condition is the

denominator or x + 2 is not 0

then X is not 0 minus two is

not negative 2 or X is not =

negative 2 well this is the domain of the function f

so the domain of the function F is x where x is

not = negative 2 and X is a member of

real numbers Now for the function GX GX is

= root x min 3 this is the root form remember

the condition inside the root cannot be

negative so X min 3 must be

more than or equal to zero then X is more

than or equal to zero plus 3 x is more

than = 3 then the domain of G is x where x

more than = 3 x members of real numbers

Now we make the number line

to determine the first intersection

X is not = negative 2 negative two

here is not equal to negative 2 so

we circle this so it doesn't go

into your friends' answers then X more

than = 3 from 3 to the right well coincidentally

negative two which is not allowed is already

outside the answer so the answer is

yes, this one friends so the

answer is the domain of FB konige is

x where x more than = 3 and X members of

real numbers Okay now we continue

How to determine the domain of the

multiplication result for example your list of functions

f and function G then the domain is the

same method is the intersection of the two functions

intersection of the domains of the two functions

Example

Hi if it is known that the effect is 3 x

squared and GSC is 1 per X min 4

Determine the domain of f * GX yes

the method is the same we find the domain of f and the

domain of G then we slice the

domain of f this quadratic form there

are no conditions so x

is all members of real numbers

while for gx1 per X min 4 because

this is a rational form remember the divisor

cannot be zero so X min 4 is not

worth 0 then X is not worth zero

plus 4 is not worth 4 then the domain of G

is x is not = negative 4 we make a

number line the domain of F is all

real numbers so we shade everything

then the domain is not worth 4

so here it cannot be worth 4 yes so like

this it doesn't enter friends then the

answer is the domain of FK Lights is

all real numbers except four so X is

not with four X members of

real numbers like this Okay we basesumatary

last is the domain of the division result

For example there is a division of F divided by ge then the

domain of frg is the domain of F

intersected with the domain of G well intersected

again with the condition friends because

here the division remember the divisor

cannot be worth zero this is the condition of the divisor

cannot be worth zero because the design of

the divisor is G style so GX is not

worth not Okay for example

if it is known that FX = 3 x squared and GX =

X min 3 Determine the origin of Ever

GX yes the domain of the effect is all members of

real numbers then GX is

x-men 3 yes here there are any conditions

because this is not a fraction

and also not a root form so the domain

of g Those are all real numbers too

then we just use the condition because

we will look for the division of F divided by ge

three this will be as a divisor

the divisor must not be zero so GX is

not zero this is the condition gxl

badge situ X min 3 x min 3 is not equal

to zero then X is not = 3 we make

our number line the third intersection the

third condition Nia when this domain

we English

the first DF domain F is all

members of real numbers means we shade

all Then DG is also the same all

members of real numbers so we

also shade all then the condition Mbak X

is not = 3 so in this art section it

cannot be as an answer does not

meet yes this does not meet then

the answer is all real numbers

except three domains never g = x where x

is x is not = 3 and X is a drill member

so the exception is x = 3 Apart from

that, you can Okay, that's all for

this video, I apologize if there are any shortcomings,

I hope this video can be useful for

friends who are studying mathematics, I am

Deni Handayani, I resign

Assalamualaikum

warohmatullohi wabarokatuh hi hi hi hi