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Thread: strict functions

  1. #1
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    strict functions

    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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    Re: strict functions

    Quote Originally Posted by franios View Post
    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

    $\displaystyle \forall a,b \in D$ 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?
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