Let and be bijections

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

Problem

Let f:A→Bf:A\to B and g:B→Cg:B\to C be bijections. For every c∈Cc\in C, which of the following is always equal to (g∘f)−1(c)(g\circ f)^{-1}(c)? (a) g−1(f−1(c))g^{-1}\bigl(f^{-1}(c)\bigr) (b) g−1(f(c))g^{-1}\bigl(f(c)\bigr) (c) f−1(g−1(c))f^{-1}\bigl(g^{-1}(c)\bigr) (d) f(g−1(c))f\bigl(g^{-1}(c)\bigr)

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