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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

  1. A \(\{-1\}\)
  2. B 0
  3. C \(\left\{-\frac{1}{2}\right\}\)
  4. D \(\phi\)
Verified Solution

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,…