Relations Question 9
Question: If $f(x)=\begin{cases}x^2, & \text { for } x \geq 0 \\ x, & \text { for } x<0\end{cases}$, then fof$(x)$ is given by
Options:
A) $x^2$ for $x \geq 0, x$ for $x<0$
B) $x^4$ for $x \geq 0, x^2$ for $x<0$
C) $x^4$ for $x \geq 0,-x^2$ for $x<0$
D) $x^4$ for $x \geq 0, x$ for $x<0$
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(f(x))= \begin{vmatrix} {{(f(x))}^{2}},forf(x)\ge 0 \\ f(x),forf(x)<0 \\ \end{vmatrix} . $ = $ \begin{vmatrix} {{(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{vmatrix} . $
$ = \begin{vmatrix} x^{4},x\ge 0 \\ x,x<0 \\ \end{vmatrix} . $
BETA
