Sets Relations And Functions Question 21
Question: If $ f(x)= \begin{cases} x^{2}, \text{for} x \ge 0 \\ x,\text{for} x<0 \\ \end{cases} , $ then fof (x) is given by
Options:
A) $ x^{2} \text{ for } x\ge 0, $ $ x \text{ for } x<0 $
B) $ x^{4}\text{ for } x\ge 0, $ $ x^{2}\text{ for } x<0 $
C) $ x^{4}\text{ for } x\ge 0, $ $ -x^{2}\text{ for } x<0 $
D) $ x^{4}\text{ for } x\ge 0, $ $ x\text{ for } x<0 $
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Answer:
Correct Answer: D
Solution:
- [d] $ f(f(x))= \begin{cases} {{(f(x))}^{2}},\text{ for } f(x)\ge 0 \\ f(x), \text{ for } f(x)<0 \\ \end{cases} . $ = $ \begin{cases} {{(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{cases} . $ $ = \begin{cases} x^{4},x\ge 0 \\ x,x<0 \\ \end{cases} . $
BETA
