# Homework Help: Compostion of functions

1. Nov 19, 2012

### nicnicman

1. The problem statement, all variables and given/known data

Suppose f : R→R and g : R→R where g(x) = 3x + 5 and g o f(x) = x^2 - 7.
Find the rule for f.

2. Relevant equations

3. The attempt at a solution

These seem pretty simple, but I want to make sure I'm on the right track.

3(f(x)) + 5 = x^2 - 7
3(f(x)) = x^2 - 12
f(x) = (x^2 - 12)/3

How does this look?

Last edited: Nov 19, 2012
2. Nov 19, 2012

### Skins

Looks correct. You could re-write f(x) as

$$f(x) \, = \, \frac{1}{3}x^{2} \, - \, 4$$

but otherwise you are correct and is fine as you have written it.

Last edited: Nov 19, 2012
3. Nov 19, 2012

### nicnicman

Okay, thanks.