Solving with composition

Question

I need help with a homework question regarding composition!

Let A = B = C = real numbers.

Let f: A -> B and g: B -> C be defined by f(a) = a-1 and g(b) = b2 [b squared!]

Find:

i. (f∘g)(x)

ii. (f∘f)(y)

Does anybody know how to solve these?

Answer 1

We have

$$(f∘g)(x) = f(g(x)) = g(x) - 1 = x^2 - 1$$

and

$$(f∘f)(y) = f(f(y)) = f(y) - 1 = y - 1 - 1 = y - 2$$