If $f:[-2,2]\to\mathbb{R}$ is defined by $f(x)=\begin{cases}-1,& -2\le x\le0 \\ x-1,& 0\le x\le2 \end{cases}$, then $\{x\in[-2,2]:x\le0 \text{ and } f(|x|)=x\}$ is
- A. $\{-1\}$
- B. $\{0\}$
- C. $\{-\tfrac{1}{2}\}$
- D. $\emptyset$
✅ Correct Answer: $\{-\tfrac{1}{2}\}$
Explanation
For $x\le0$, $|x|=-x$. Then $f(|x|)=(-x)-1$. Set $(-x)-1=x \Rightarrow x=-\tfrac{1}{2}$. Hence set={$-\tfrac{1}{2}$}.
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