Question

Compositions of Functions
Given: f(x) =2x+7 g(x) = x^2 h(x) = x-1

Now they want me to solve h(g(x)) but before I can do that, I need to know how to write out the problem :( can someone please help me?

Answer 1

Basically, you start off with the function h(x) which is x-1, so wherever you see an x in h(x) you replace with g(x) which is x^2.

I'll give you an example, and then try to do the one you are having a problem with.

h(x)=2x-7
g(x)=5x

h[g(x)] = 2(5x)-7 =10x-7

Do you understand?

Answer 2

@SaoLao

Answer 3

So then since I'm putting g(x) in the place of h(x) would it be x^2 - 1?

Answer 4

Yes, that is correct.

Answer 5

Now, can I test to see if you understood?
With the same functions you wrote:
f(x) =2x+7 g(x) = x^2 h(x) = x-1

what is g[f(x)]?

Answer 6

Thank you! & oh okay. I think it would be 2x(x^2)+7?

Answer 7

Are you sure about that?
remember, wherever you see an x the entire function f(x) replaces it think of f(x)=(2x+7)

Answer 8

(2x+7)^2?

Answer 9

Exactly!

Answer 10

When you foil that it should give 4x^2 + 28x + 49

Answer 11

so all i had to do is plug in for x with whatever the second function is?

Answer 12

yep!

Answer 13

Oh okay i get it thank you! So then what if you had three functions?

Answer 14

Would you still have to do that same thing?

Answer 15

That's a good question and I'm not 100% sure so I wouldn't want to say something and confuse you. Here are some resources for you to try and find the answer, otherwise ask your teacher lol
http://www.mathsisfun.com/sets/functions-composition.html
http://www.youtube.com/watch?v=p1G9C0R4Z9c

Answer 16

oh okay its ok thank you! :) you've been a lot of help :D

Answer 17

:) no problem. good work!