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

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- Oct 22nd 2012, 07:13 PMfraniosstrict functions
Prove that if f is strictly increasing on a domain, D, then its inverse f

^{-1}is strictly increasing on f(D). - Oct 23rd 2012, 04:59 AMTheEmptySetRe: strict functions
This follows directly from the defintions.

A function is strictly increasing if

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

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

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

You just need to show for all $\displaystyle c,d \in f(D)$ if $\displaystyle c <d \iff f^{-1}(c) < f^{-1}(d)$

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