Question

Let f (x) = 5x^2 + 7 and g(x) = x – 3.
(a) Find the composite function ( f o
g)(x) and simplify. Show work.
(b) Find ( f o
g ) (2)
can anyone tell me if a.) =5x^3+7x-3
and if b.) =24?

Thanks!

Answer 1

Mind telling me how you got your answer to (a) ?

Answer 2

f(g(x))= f(5x^2+7)
x(5x^2+7)-3
5x^3+7x-3
maybe?

Answer 3

Let me walk you through it, aye?\[\Large f(\color{red}x)=5\color{red}x^2+7\]\[\Large g(\color{green}x) = \color{green}x-3\]

Answer 4

ok thanks

Answer 5

Now, \[\Large (f\circ g)(\color{blue}x) = f(\color{red}{g(x)})\]This, you know, right?

Answer 6

yes

Answer 7

So what I want you to do for now is replace all instances of \(\color{red}x\) in \(f(\color{red}x)\) with \(\color{red}{g(x)}\)

Like so:
\[\Large f(\color{red}x) =5\color{red}x^2+7\]\[\Large f(\color{red}{g(x)}) = \color{blue}?\]

Answer 8

well x-3 into 5x^2+7 right?

Answer 9

That is correct...

Answer 10

but I thought I did that, must have written it wrong

Answer 11

Then show me what you have written, let's see if we can pinpoint the error, if there is one.

Answer 12

x(5x^2+7)-3 wrong?

Answer 13

Yup.
Take it slow... truth is it's far simpler than that.
\[\Large f(\color{red}{g(x)}) = f(\color{red}{x-3})\]

Answer 14

5(x-3)^2+7

Answer 15

That's much better :)
Simplify.

Answer 16

5(x^2-6x+9)+7?

Answer 17

Good so far... now distribute the 5 within the parentheses, and then simplify further.

Answer 18

5x^2-30x+52?

Answer 19

Bingo :)
\[\Large (f\circ g)(\color{blue}x)=5\color{blue}x^2-30\color{blue}x+52\]
That wasn't so bad, was it?
Now find \[\Large (f\circ g)(\color{blue}2)\]

Answer 20

12?

Answer 21

wait never mind

Answer 22

Pardon?

Answer 23

thats not right

Answer 24

If it isn't, then correct it.

Answer 25

i think its 10

Answer 26

You think? But are you sure?
(This is arithmetic, don't go wrong on me now XD )

Answer 27

\[\Large (f\circ g)(\color{blue}2) = 5(\color{blue}2)^2 - 30(\color{blue}2) + 52\]

Answer 28

ok i did have it right!

Answer 29

Yes you did... you had me worried there.

Job (almost) well done :)

Good luck with the rest XD
(If any)
signing off now...

-------------------------------------------------
Terence out

Answer 30

THANK YOU!!!!!!!!!!!

Answer 31

@autumn_sky hope this helps