TS EAMCET · Maths · Functions
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
- C \(\left\{-\frac{1}{2}\right\}\)
- D \(\phi\)
Answer & Solution
Correct Answer
(C) \(\left\{-\frac{1}{2}\right\}\)
Step-by-step Solution
Detailed explanation
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,…
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