Question

If F -1(x) is the inverse of F(x), which statements must be true?

Answer 1

The inverse function, denoted $F^{-1}(x),$ of a one-to-one function $F(x)$ is defined as

$F^{-1}(x) = \{(y,x) | \text{ such that } y = f(x)\}.$

Main properties:

1. $F(F^{-1}(x)) = x,$ x in the domain of $F^{-1};$

$F^{-1}(F(x)) = x,$ x in the domain of F.

2. The domain of F is equal to the range of  $F^{-1}$ and the range of F is equal to the domain of  $F^{-1}.$

From these properties you can state that options B, C, D and E are true and points A and F are false.