Here are some exercises for your practice.

Suppose f(x) = (x-1)^2 - 1. Determine the following.
1. f(0) = ?
2. f(1) = ?
3. f(y) = ?
4. f(x^2) = ?
5. f(1/x) = ?
6. f(f(x)) = ?
7. Given g(x) = 1-x, what is f(g(x))?
8. Given g(x) = 1-x, what is g(f(x))?
9. Given f(g(x)) = x^2 + 4x + 3, and suppose g(x) = ax+b is linear. What are the constants a and b?
10. Given g(f(x)) = -2x^2 + 4x + 1, and suppose g(x) = ax+b is linear. What are the constants a and b?