Q4 if the function f; 1,∞→1,∞ is defined by f (x) = 2xx-1 , then f-1 (x) is (A) - Maths - Relations and Functions

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Q4 if the function f; 1 , ∞ → 1 , ∞ is defined by
f (x) = 2 x x - 1 , then f - 1 (x) is
(A) 1 2 x ( x - 1 )
(B) 1 2 1 + 1 +   4   log 2     x
(C) 1 2 1   -   1 +   4   log 2   x
(D) not defined

Sakshi Naik · Answer

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Q4. if the function f; 1 , ∞ → 1 , ∞ is defined by f (x) = 2 x x - 1 , then f - 1 (x) is (A) 1 2 x ( x - 1 ) (B) 1 2 1 + 1 + 4 log 2 x (C) 1 2 1 - 1 + 4 log 2 x (D) not defined

Q4. if the function f; $[1, \infty) \to (1, \infty)$ is defined by f (x) = $2^{x (x - 1)}$ , then f $^{- 1}$ (x) is
(A) ${(\frac{1}{2})}^{x (x - 1)}$
(B) $\frac{1}{2} [1 + \sqrt{1 + 4 \log_{2} x}]$
(C) $\frac{1}{2} (1 - \sqrt{1 + 4 \log_{2} x})$
(D) not defined