Question

Suppose that f (x )is the inverse of g (x )and g (x )is the inverse of f (x ). Then f (g (x ))equals

Answer 1

Since f(x) is the inverse of g(x) and g(x) is the inverse of f(x), then by definition

`(f\circ g)(x)=f(g(x))=x\\(g\circ f)(x)=g(f(x))=x`

Answer 2

f(g(x)) = x

Explanation:

The inverse of a function is a function that "reverses" the other one, meaning that if I input a value x to the first function and get the result y on the second function, I can put the same y value to the second function and it will give me the first x value again.

In this problem we have that:

f(x) is the inverse of g(x) ⇒ f (x) = g⁻¹(x)

g(x) is the inverse of f(x) ⇒ g(x) = f ⁻¹(x)

The problem asks us to find f(g(x))

f(g(x)) = f(f ⁻¹(x)) = x

Therefore, f(g(x)) = x