Question

For each pair of functions f and g below, find f(g(x)) and g(f(x)).
Then, determine whether f and g are inverses of each other.

Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)
(a) f(x)=-4x
g(x)=1/4x, x neq 0
f(g(x))
g(f(x))
b) f(x)=1/3x, x neq 0
g(x)= 1/3x, x neq 0
f(g(x))
g(f(x))

Answer 1

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

Answer 2

B
f(g(x))=1/(3*1/3x)=x
g(f(x))=1/(3*1/3x)=x