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JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1
Suppose f:[−2,  2]→Rf:\left[ { - 2,\;2} \right] \to R is defined by
f(x)={−1,  for−2≤x≤0x−1  for  0≤x≤2f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} { - 1,\;for - 2 \le x \le 0}\\ {x - 1\;for\;0 \le x \le 2} \end{array}} \right., then {x∈[−2,  2]:x≤0  and  f(∣x∣)=x}\left\{ {x \in \left[ { - 2,\;2} \right]:x \le 0\;\mathrm{and}\;f\left( {\left| x \right|} \right) = x} \right\} is equal to
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Correct option: C
{−12}\left\{ { - \frac{1}{2}} \right\}
Option C ({−12}\left\{ { - \frac{1}{2}} \right\}) is correct because it represents the solution to the equation f(∣x∣)=xf(|x|) = x within the given domain and condition.

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