Define the functions

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Define the functions f(x)={x2,x≤1,2x+1,x>1,g(x)=x−2  (x≥2).f(x)=\begin{cases}x^{2}, & x\le 1,\\2x+1, & x>1,\end{cases}\qquad g(x)=\sqrt{x-2}\;(x\ge2). (i) Write the range of ff. (ii) Construct the composition (g∘f)(x)(g\circ f)(x), showing working for each piece that arises. (iii) Determine the domain of (g∘f)(g\circ f) and write the composition as a single piecewise function over this domain.

Related theory

Browse the problem library