Q92 / 160 · TS EAMCET 2003 · Mathematics

Suppose $\quad f:[-2,2] \rightarrow R \quad$ is defined by $f(x)=\left\{\begin{array}{ccc}-1, & \text { for } & -2 \leq x \leq 0 \\x-1, & \text { for } & 0 \leq x \leq 2 \\\{x \in[-2,2]: x \leq 0 & \text { and } & f(|x|)=x\end{array}\right.$ is equal tos

  • A
    $\{-1\}$
  • B
    0
  • Correct answer
    C
    $\left\{-\frac{1}{2}\right\}$
  • D
    $\phi$

Solution

We have, $f(x)=\left\{\begin{array}{c}-1, \text { for }-2 \leq x \leq 0 \\x-1, \text { for } 0 \leq x \leq 2\end{array}\right.$ Now, take $x=-\frac{1}{2}$ $\therefore \quad f\left(\left|-\frac{1}{2}\right|\right)=f\left(\frac{1}{2}\right)=\frac{1}{2}-1=-\frac{1}{2}$ Hence, $\quad f(|x|)=x$ $\therefore \quad$ Domain of $f(x)=\left\{-\frac{1}{2}\right\}$

Hence, the correct answer is option: 'C'.

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