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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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If $f(x)=(4-(x-7)^3\},then\;f^{-1}(x)$=____________.

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  • we define $f^{-1}(x)$ as a function .
  • such that $(fof^{-1})(x)=x$ ie $g=f^{-1}$ is the inverse function of f if $fog=gof =I$
Let $y=4-(x-7)^3$
we define a function g(y) such that $g(y)=(4-y)^{1/3}+7$
we see that $(fog)(y)=f((4-y)^{1/3}+7)$
Hence y is inverse of f
and $g(x)=f^{-1}(x)=(4-x)^{1/3}+7$


answered Mar 6, 2013 by meena.p

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