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

Correct option is 2121+1+4log2⁡x

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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

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(1/2)x(x−1)

121+1+4log2⁡x

121-1+4log2⁡x

not defined

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detailed solution

Correct option is B

Let f(x)=y=2x(x−1)⇒ log⁡y=x(x−1)log2⇒ x2−x−log2⁡y=0⇒ x=1±1+4log2⁡y2⇒ x=f−1(y)=1±1+4log2⁡y2⇒f−1(x)=1+1+4log2⁡y2 as f−1(x)≥1.

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

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Ready to Test Your Skills?

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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