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MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider f:x↦2xf:x\mapsto2x and g:x↦4x−3g:x\mapsto4x-3. (a) Find (f∘g)(x)(f\circ g)(x). (b) Given (f∘g)−1(k)=2(f\circ g)^{-1}(k)=2, find kk. (c) Show that (f−1∘g−1)(x)=(g∘f)−1(x)(f^{-1}\circ g^{-1})(x)=(g\circ f)^{-1}(x).

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