The inverse of the function f(x)=[1−(x−4)5]19 is

Let [1−(x−4)5]19=y⇒1−(x−4)5=y9⇒x=4+(1−y9)15 f-1(x)=4+(1−x9)15

The inverse of the function f(x)=[1−(x−4)5]19 is

Let [1−(x−4)5]19=y⇒1−(x−4)5=y9⇒x=4+(1−y9)15 f-1(x)=4+(1−x9)15

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The inverse of the function $f (x) = {[1 - {(x - 4)}^{5}]}^{\frac{1}{9}}$ is

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$4 + {(1 - x^{9})}^{\frac{1}{5}}$

${(1 - x^{9})}^{\frac{1}{5}} - 4$

$5 + {(1 - x^{4})}^{9}$

$4 - {(1 - x^{9})}^{5}$

answer is A.

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Detailed Solution

Let ${[1 - {(x - 4)}^{5}]}^{\frac{1}{9}} = y \Rightarrow 1 - {(x - 4)}^{5} = y^{9} \Rightarrow x = 4 + {(1 - y^{9})}^{\frac{1}{5}}$

$f^{- 1} (x) = 4 + {(1 - x^{9})}^{\frac{1}{5}}$

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The inverse of the function f(x)=[1−(x−4)5]19 is

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The inverse of the function $f (x) = {[1 - {(x - 4)}^{5}]}^{\frac{1}{9}}$ is