Question

Pre-calculus please help and please explain

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x

f(x)= 4/x and g(x)= 4/x

Answer 1

We have to make sure the functions are simplified into just x to verify that they are inverses. To do this, we have to compose the functions into each other.

f(g(x)) = 4/(4/x)

The 4's cancel out and you're left with just x

f(g(x)) = x

Let's compose f(x) into g(x) now.

g(f(x)) = 4/(4/x)

The 4's cancel out and you're left with just x

Since both functions are equal to x after composing them into each other, we can confirm that they are indeed inverses of each other.