Question

Please help! I’m in a test rn! 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 (The • means f of g)


D.) (g•f)(x) = x

Answer 1

D)
`(g\cdot f)(x)=x`

Explanation:

If two functions
`f(x)` and
`g(x)` are inverse of each other, then the following conditions must be true:

i.
`(f\cdot g)(x)=x`

ii.
`(g\cdot f)(x)=x`

Therefore, out of the four choices available, only option D matches the condition for inverse function to exist.

Therefore,
`(g\cdot f)(x)=x`