Let be bijective with inverse

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

Problem

Let f:R∖{3}→R∖{2}f: \mathbb{R}\setminus\{3\}\to \mathbb{R}\setminus\{2\} be bijective with inverse f−1f^{-1}. Identify the composition that equals the identity function on R∖{3}\mathbb{R}\setminus\{3\}. (a) f∘f−1f\circ f^{-1} (b) f−1∘IR∖{2}f^{-1}\circ I_{\mathbb{R}\setminus\{2\}} (c) f−1∘ff^{-1}\circ f (d) f∘IR∖{3}f\circ I_{\mathbb{R}\setminus\{3\}}

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