Question

PLEASE HELP! If f(x) and g(x) are inverse functions of each other, which of the following statements is true?

A.) f(x) *divided by* g(x) = 1


B.) f(x) = -g(x)


C.) (f•g)(x) = 1 (• does not mean times, it means f of g)


D.) (g•f)(x) = x

Answer 1

(g•f)(x) = x.

Explanation:

Let
`f(x) = x^(2) + 1`, then the inverse function of the f(x) is
`g(x) = √(x - 1)`

So, (g•f)(x) =
`g[f(x)] = g(x^(2) + 1 ) = \sqrt{(x^(2) + 1) - 1} = \sqrt{x^(2) } = x`

Therefore, we can write if f(x) and g(x) are inverse functions of each other, then (g•f)(x) = x.

Hence, option D is correct. (Answer)