Which statement verifies that f(x) and g(x) are inverses of each other?

Question

f(g(x)) = x
f(g(x)) = x and g(f(x)) = –x
f(g(x)) = g(f(x)
f(g(x)) = x and g(f(x)) = x

Answer 1

The test to verify if a function f is the inverse of another function g is given by using the composition of the functions such as this, f(g(x))= x. Therefore, to answer your question,

• f(g(x))=x is saying f is the inverse of g.
• f(g(x))=x is saying f is the inverse of g but g is not the inverse of f, g(f(x))≠x.
• f(g(x))= g(f(x)) is saying the composition of functions f(g(x)) is equal to the composition of functions g(f(x)), but not necessarily inverses. It doesn't specify each equals x.
• f(g(x))=x and g(f(x)) =x is saying f is the inverse of g and g is the inverse of f.