Suppose $f:\left[ { - 2,2} \right] \to R$ is defined by $f\left( x \right) = \left\{ {\;\begin{array}{*{20}{c}} { - 1\;{\rm{for}} - 2 \le x \le 0}\\ {x - 1\;{\rm{for}}\;0 \le x \le 2} \end{array}} \right.$ then $\left\{ {x \in \left[ { - 2,2} \right]:x \le 0\;{\rm{and}}\;f\left( {\left| x \right|} \right) = x} \right\} = $

JEE MATHEMATICS MCQ: FUNCTIONS

1 Hard

1 of 1

Application +4 | -1

Suppose

f:\left[ { - 2,2} \right] \to R

is defined by

f\left( x \right) = \left\{ {\;\begin{array}{cccccccccccccccccccc} { - 1\;\mathrm{for} - 2 \le x \le 0}\\ {x - 1\;\mathrm{for}\;0 \le x \le 2} \end{array}} \right.

then

\left\{ {x \in \left[ { - 2,2} \right]:x \le 0\;\mathrm{and}\;f\left( {\left| x \right|} \right) = x} \right\} =

View answer and explanation

Correct option: C

\left\{ { - 1/2} \right\}

Option C ({-1/2}) is correct because it is the only value that satisfies the given conditions and falls within the specified interval.