Let f(x) defined on [ -2, 2] and is given by f(x)= array ll -1, & -2 x 0 x-1, & 0 x 2…
Mathematics · JEE Main · NTA Exams — Sets, Relations and Functions
Let \(f(x)\) defined on [ -2, 2] and is given by
\(f(x)=\left\{\begin{array}{ll} -1, & -2 \leqslant x \leqslant 0 \\ x-1, & 0 \leqslant x \leqslant 2 \end{array}\right\}\)
and \(g(\mathbf{x})=f|\mathbf{x}|+|f(\mathbf{x})|\). Then find \(g(x)\)
- \(g(x)=\left\{\begin{array}{ll} 1_{1} & x \geqslant 0 \\ -1_{1} & 0<0 \\ 0, & x=0 \end{array}\right.\)
- \(g(x)=\left\{\begin{array}{lr} 1, & x=0 \\ 1-x_{1} & x<0 \\ 1+x_{1} & x>0 \end{array}\right.\)
- \(g(x)=\left\{\begin{array}{lr} -x, & -2 \leq x \leq 0 \\ 0, & 0 \leq x \leq 1 \\ 2(x-1) 1 \leq x \leq 2 \end{array}\right.\)
- None of these
Answer
(D) None of these
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