# Math Help - strict functions

1. ## strict functions

Prove that if f is strictly increasing on a domain, D, then its inverse f-1 is strictly increasing on f(D).

2. ## Re: strict functions

Originally Posted by franios
Prove that if f is strictly increasing on a domain, D, then its inverse f-1 is strictly increasing on f(D).
This follows directly from the defintions.

A function is strictly increasing if

$\forall a,b \in D$ if $a < b \iff f(a) < f(b)$

What is the domain of $f^{-1}(x)$?

What is the range of $f^{-1}(x)$?

You just need to show for all $c,d \in f(D)$ if $c

Can you show the defintion for the inverse holds using the above?