A) \[{{x}^{2}}for\,x\ge 0,\,\]\[x\text{ }for\text{ }x<0\]
B) \[{{x}^{4}}for\,x\ge 0,\,\]\[{{x}^{2}}for\text{ }x<0\]
C) \[{{x}^{4}}for\,x\ge 0,\,\]\[-{{x}^{2}}for\text{ }x<0\]
D) \[{{x}^{4}}for\,x\ge 0,\,\]\[x\text{ }for\text{ }x<0\]
Correct Answer: D
Solution :
[d] \[f(f(x))=\left\{ \begin{matrix} {{(f(x))}^{2}},\text{for}\,f(x)\ge 0 \\ f(x),\,\,\,\text{for}\,\,f(x)<0 \\ \end{matrix} \right.\] =\[\left\{ \begin{matrix} {{({{x}^{2}})}^{2}},{{x}^{2}}\ge 0,x\ge 0 \\ {{x}^{2}},\,\,x\ge 0,\,\,x<0 \\ {{x}^{2}},\,\,{{x}^{2}}<0,\,\,x\ge 0 \\ x,\,\,x<0,\,\,x<0 \\ \end{matrix} \right.\] \[=\left\{ \begin{matrix} {{x}^{4}},\,\,x\ge 0 \\ x,\,\,x<0 \\ \end{matrix} \right.\]
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