Define the functions f(x)= cases x+2, & x 2

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

Problem

Define the functions f(x)={x+2,x≤2,x−2,x>2,g(t)=1t−4  (t≠4).f(x)=\begin{cases} x+2, & x\le 2,\\ \sqrt{x-2}, & x>2, \end{cases} \qquad g(t)=\dfrac{1}{t-4}\;(t\ne 4). Determine the domain of the composition g∘fg\circ f. (a) (−∞,2)∪(2,18)∪(18,∞)(-\infty,2)\cup(2,18)\cup(18,\infty) (b) R∖{18}\mathbb R\setminus\{18\} (c) R∖{4}\mathbb R\setminus\{4\} (d) R∖{2}\mathbb R\setminus\{2\}

Related theory

Browse the problem library