If the function is defined by

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

If the function f:[1,∞)→[1,∞)f:[1,\infty)\to[1,\infty) is defined by f(x)=2x(x−1)f(x)=2^{x(x-1)}, then f−1(x)f^{-1}(x) is (a) (12)x(x−1)\left(\frac{1}{2}\right)^{x(x-1)} (b) 12(1+1+4log⁡2x)\frac{1}{2}\left(1+\sqrt{1+4\log_2 x}\right) (c) 12(1−1+4log⁡2x)\frac{1}{2}\left(1-\sqrt{1+4\log_2 x}\right) (d) Not defined

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