If the function f:$$1$$,∞→$$1$$,∞ is defined by $$f(x)=2xx$$−$$1$$ then f−$$1(x)$$ is

Correct option is 2121+1+4log2x

Questions

If the function $f : [1, \infty) \to [1, \infty)$ is defined by $f (x) = 2^{x (x - 1)} then f^{- 1} (x)$ is

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12x(x−1)

121+1+4log2x

121−1+4log2x

121±1+4log2x

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detailed solution

Correct option is B

y=2x(y−1)⇒xx−1=log2y⇒x2−x−log2y=0∴ x=1±1+4log2y2∴ f−1(x)=121+1+4log2y ∵x≥1

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If the function f:1,∞→1,∞ is defined by f(x)=2xx−1 then f−1(x) is

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If the function $f : [1, \infty) \to [1, \infty)$ is defined by $f (x) = 2^{x (x - 1)} then f^{- 1} (x)$ is