Question

find f(g(x))

f(x) = 4x - 7

g(x) = 2x - 5

is it
f(g(x)) = 8x - 12 ?

Answer 1

@SolomonZelman

Answer 2

g(-5x) = -15x-5

Answer 3

this is how you get that answer

Answer 4

\(\large\color{black}{ \displaystyle \color{red}{f(x)} = \color{red}{4x - 7 } }\)
\(\large\color{black}{ \displaystyle \color{blue}{g(x)} = \color{blue}{2x - 5 } }\)

\(\large\color{black}{ \displaystyle \color{red}{f(\color{blue}{g(x)})} = \color{red}{4(\color{blue}{2x - 5 })- 7 } }\)

Answer 5

= f(3x - 5)
= -5(3x - 5)
= -15x + 25
= 25 - 15x

g[f(x)]
= g(-5x)
= 3(-5x) - 5
= -15x - 5

Answer 6

see how I am plugging the g(x) into the f(x) ?

Answer 7

then you just need to simplify.

Answer 8

yes what comes after

Answer 9

8x - 5 - 7 ?

Answer 10

then 8x - 12

Answer 11

ok

Answer 12

we will expand the parenthesis.

\(\large\color{black}{ \displaystyle \color{red}{f(\color{blue}{g(x)})} = \color{red}{4(\color{blue}{2x - 5 })- 7 } }\)

\(\large\color{black}{ \displaystyle \color{red}{f(\color{blue}{g(x)})} = \color{red}{4} \times \color{blue}{2x } +\color{red}{4} \times \color{blue}{(-5) ~~-7 } }\)

Answer 13

Again, I am multiplying everything in the parenthesis times 4. By doing so I am expanding the parenthesis.

Answer 14

can you finish simplifying the left side?

Answer 15

the right** side

Answer 16

8x + 4 * 35

Answer 17

8x + 140 ?

Answer 18

wow

Answer 19

you are first multiplying the 4 timers (-5) and then subtracting -7.

Answer 20

*times*

Answer 21

8x + -20 - 7

Answer 22

?

Answer 23

yes, you multiplied correctly, now subtract

Answer 24

-20-7=?

Answer 25

-27

Answer 26

so the answer is 8x + -27 ?

Answer 27

yes, but you can re-write it better

Answer 28

+-27 is same as just -27

Answer 29

instead of having +- there

Answer 30

so 8x - 27

Answer 31

yes

Answer 32

lagging-:(
yw

Answer 33

what about f^-1(x)

Answer 34

inverse function of this new f(g(x)), or inverse function of the f(x) or/and g(x) ?

Answer 35

you want just inverse of f(x) ?

Answer 36

yes f(x)

Answer 37

I will give you an abstract example.

Answer 38

its x + 7 / 4 right ?

Answer 39

yes

Answer 40

(x+7)/4

Answer 41

ok then thanks

Answer 42

I guess no need for abstract example:)
You got it!