Composite Functions

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August 22nd 2009, 04:28 PM
Coolman

Composite Functions

http://i28.tinypic.com/2mr9rmt.jpg
August 22nd 2009, 05:45 PM
ynj

$f(x)=x^3$
generally, if $g(x)$ is invertible, then $g^{-1}(g(f(x)))=g^{-1}(\sqrt{2-x^3})=f(x)$
August 22nd 2009, 06:21 PM
Coolman

Thanks, one more I don't get is:

http://i25.tinypic.com/2yjugdg.jpg
August 22nd 2009, 06:25 PM
ynj

Quote:

Originally Posted by Coolman

Thanks, one more I don't get is:

http://i25.tinypic.com/2yjugdg.jpg

use the same method, let $x=g^{-1}(y),f(g(x))=f(g(g^{-1}(y)))=f(y)=(g^{-1}(y))^2$

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