CBSE

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Define f:[0,∞)→[2,∞)f:[0,\infty)\to[2,\infty) by f(x)=x2+2f(x)=x^{2}+2. (a) Prove that ff is bijective. (b) Find f−1f^{-1} and state its domain and co-domain. (c) Show that f−1(f(x))=xf^{-1}\bigl(f(x)\bigr)=x for all x∈[0,∞)x\in[0,\infty) and that f(f−1(y))=yf\bigl(f^{-1}(y)\bigr)=y for all y∈[2,∞)y\in[2,\infty).

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