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  4. If f(x)=[1-(x-3)4]1/7 , find f-1(x) .

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Q. If $ f(x)={{[1-{{(x-3)}^{4}}]}^{1/7}} $ , find $ {{f}^{-1}}(x) $ .

Jharkhand CECEJharkhand CECE 2012

Solution:

Let $ y=f(x)={{[1-{{(x-3)}^{4}}]}^{1/7}} $
$ \Rightarrow $ $ {{y}^{7}}=1-{{(x-3)}^{4}} $
$ \Rightarrow $ $ {{(x-3)}^{4}}=1-{{y}^{7}} $
$ \Rightarrow $ $ x=3+{{(1-{{y}^{7}})}^{1/4}} $
$ \Rightarrow $ $ {{f}^{-1}}(y)=3+{{(1-{{y}^{7}})}^{1/4}} $
$ \Rightarrow $ $ {{f}^{-1}}(x)=3+{{(1-{{x}^{7}})}^{1/4}} $