Let be given by and by

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

Problem

Let f:R→Rf:\mathbb R\to\mathbb R be given by f(x)=3x+2f(x)=3x+2 and g:R→Rg:\mathbb R\to\mathbb R by g(x)=x3−1g(x)=x^{3}-1. The expression for (g∘f)−1(y)(g\circ f)^{-1}(y) is (a) y−13+23\dfrac{\sqrt[3]{y-1}+2}{3} (b) y+13−23\dfrac{\sqrt[3]{y+1}-2}{3} (c) y3−23\dfrac{\sqrt[3]{y}-2}{3} (d) 3y+13−23\sqrt[3]{y+1}-2

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