Question

Composite functions?

Answer 1

@jim_thompson5910

Answer 2

Recall that \[\Large (f \circ g)(x) = f(g(x))\]

Answer 3

yes i know how to do that

Answer 4

Start with f(x). Replace every x with g(x).

\[\Large f(x) = \sqrt[3]{x+2}\]
\[\Large f({\color{red}{x}}) = \sqrt[3]{{\color{red}{x}}+2}\]
\[\Large f({\color{red}{g(x)}}) = \sqrt[3]{{\color{red}{g(x)}}+2}\]

Answer 5

so we end up with `g(x)+2` and we want that to be equal to `x+3`

so set the two expressions equal to one another and isolate g(x)

Answer 6

g(x) + 2 = x+3

g(x) = ????

Answer 7

x+1?

Answer 8

yep

Answer 9

ok can u help with one more?

Answer 10

sure

Answer 11

howve you been its been forever haha

Answer 12

I'm doing well. How about you?

Answer 13

the same idea will apply here

but now we have 3 functions this time

Answer 14

pretty good busy i work 12 hours everyday and take 7 classes online so im pretty stressed

Answer 15

the inner most function is h(x)
replace every x in h(x) with 4. Then evaluate to get what?

Answer 16

sq rt of 4?

Answer 17

2?

Answer 18

`i work 12 hours everyday and take 7 classes online`
that sounds like an impossible task, but somehow you're making it work

Answer 19

yes the square root of 4 is 2

Answer 20

now you'll plug that into g(x)

Answer 21

yeah somehow couldnt tell you how haha but 7?

Answer 22

plug x = 2 into g(x) to get ???

Answer 23

yep 7

Answer 24

okay then what

Answer 25

then that result is fed into f(x)

Answer 26

it's like a chain reaction

Answer 27

so 28

Answer 28

yep

Answer 29

awwesome is this correct btw?