Question

solved!

Answer 1

Start by picking two functions g(x) and f(x).

Answer 2

f(g(x))

Answer 3

? still confused

Answer 4

You first have to come up with 2 functions on your own, f(x) and g(x) as they mention in the question.

Answer 5

f(x)=-3x+21
g(x)=x^2-9
??

Answer 6

Ok, good choices. Now f(g(x)) means you take your f(x) function, and where ever you see an x, you replace it with the equation for g(x).

Answer 7

so where do I go from there?

Answer 8

So you should have f(g(x)) = -3(x^2 - 9) + 21 ?
From there you can expand the brackets to simplify it a bit more.

Answer 9

ok so then after its simplified, I'm done?

Answer 10

Now you have your f(g(x)). You need to do the same thing for g(f(x)), but replacing all the x's in the equation of g(x) with the equation for f(x).

Answer 11

my head hurts. i'm trying really hard to understand, but I'm not sure.

Answer 12

Show me your work for g(f(x)) and I'll help you out :P

Answer 13

ok one sec

Answer 14

-3x^2+48 is the first one??

Answer 15

after its simplified

Answer 16

Perfect!

Answer 17

okay so how exactly do i set up the second one?

Answer 18

Take your g(x) = x^2-9, and wherever there is an x, replace that with -3x+21.

Answer 19

I have a feeling this is wrong, but I got -3x^2+432

Answer 20

It's a bit wrong, I have a feeling it is where you expanded your exponent (namely the x^2 and x term).

Answer 21

is it cubed instead of squared?

Answer 22

Nope, should still be x^2 because you still only have one x inside of the square, did you get to this step ok?
g(f(x)) = (-3x+21)^2 - 9

Answer 23

3x^2+432

Answer 24

9x^2=432

Answer 25

*+432

Answer 26

Let's look at the expansion of (-3x+21)^2, We have:
(-3x+21)(-3x+21)
(-3x)(-3x) + (-3x)(21) + (21)(-3x) + 21(21)

Answer 27

There you should see how you are missing the x term.

Answer 28

so frustrated

Answer 29

It's ok just take it slow. What do you get when you expand and simplify:

(-3x)(-3x) + (-3x)(21) + (21)(-3x) + 21(21)

Answer 30

9x-63x-63x=441

Answer 31

9x^2-63x-63x+441 is good! Combine your -63x and -63x to get -126. And we have:
9x^2 -126x+441.

But that is only our (-3x+21)^2, so we still have to do the subtract 9 since g(f(x)) = (-3x+21)^2 - 9.

So the final answer will become g(f(x)) = 9x^2 -126x+441 - 9 = 9x^2 -126x+423

Answer 32

ok awesome so wich composite function has the greatest value for x = 10?

Answer 33

*which

Answer 34

That's simple. Just plug your 10 into f(g(x)) and g(f(x)) and see which has the higher value.

Answer 35

g?

Answer 36

You got it.

Answer 37

nice! thank you so much

Answer 38

Noo problem!