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1.Relation and Function
easy
Suppose $f:[2,\;2] \to R$ is defined by $f(x) = \left\{ \begin{array}{l} - 1\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{for}}\; - 2 \le x \le 0\\x - 1\;\;\;\;\;{\rm{for}}\;0 \le x \le 2\end{array} \right.$, then $\{ x \in ( - 2,\;2):x \le 0$ and $f(|x|) = x\} = $
A
$\{ - 1\} $
B
${0}$
C
$\{ - 1/2\} $
D
$\phi $
Solution
(c) By verification, $f\left( {\left| { – \frac{1}{2}} \right|} \right) = f\left( {\frac{1}{2}} \right) = \frac{1}{2} – 1 = – \frac{1}{2}$
Hence $f(|x|) = x$.
Standard 12
Mathematics
