.

Question

Question 3 options:

Given g(x)=−x/4+4 and f(x)=4x+1/4 , find g^-1(x) , f^-1(x) , (g∘f)^-1(x) and (f^−1∘g^-1)(x) . What can you conclude?

Answer 1

g^-1(x) = 16-4x
f^-1(x) = x/4 - 1/16

(g∘f)^-1 = 63/16 - x
(f^-1 ∘ g^-1)(x) = (16-4x)/4-1 = 63/16 - x

It is not hard to show that
(g∘f)^-1(x) = (f^−1∘g^-1)(x)

works with matrices as well:

(AB)^-1 = B^-1 A^-1