JEE Mains · Maths · STD 12 - 1. relation and function
If \(f(x)=\left\{\begin{array}{l}2+2 x,-1 \leq x < 0 \\ 1-\frac{x}{3}, 0 \leq x \leq 3\end{array}\right.\) and \(g(x)=\left\{\begin{array}{l}-x,-3 \leq x \leq 0 \\ x, 0 < x \leq 1\end{array}\right.\)then range of \((fog (X))\) is
- A \((0,1]\)
- B \([0,3)\)
- C \([0,1]\)
- D \([0,1)\)
Answer & Solution
Correct Answer
(C) \([0,1]\)
Step-by-step Solution
Detailed explanation
\(f(g(x))= \begin{cases}2+2 g(x) & ,-1 \leq g(x)<0 \\ 1-\frac{g(x)}{3}, & 0\leq g(x) \leq 3\end{cases}\) By \((1)\) \(x \in \phi\) And by \((2)\) \(x \in[-3,0]\) and \(x \in[0,1]\) Range of \(f(g(X))\) is \([0,1]\)
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