Let be a bijective function with inverse

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let ff be a bijective function with inverse f−1f^{-1}. Which of the following expressions is equal to xx for all xx in the appropriate domain? (a) f−1(f(f(x)))f^{-1}\bigl(f(f(x))\bigr) (b) f(f−1(x))f\bigl(f^{-1}(x)\bigr) (c) f(f(x))f\bigl(f(x)\bigr) (d) f−1(f−1(x))f^{-1}\bigl(f^{-1}(x)\bigr)

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