For an invertible function with inverse

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

Problem

For an invertible function f:A→Bf:A\to B with inverse f−1f^{-1}, which of the following identities is ALWAYS true for every x∈Ax\in A? (a) f(f−1(x))=xf\bigl(f^{-1}(x)\bigr)=x (b) f(f(x))=xf\bigl(f(x)\bigr)=x (c) f−1(f(x))=xf^{-1}\bigl(f(x)\bigr)=x (d) f−1(x)=f(x)f^{-1}(x)=f(x)

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