Let $$f(x)$$ be defined on [−$$2$$,$$2$$] and is given by $$f(x)=$$−$$1$$,−$$2$$≤x≤$$0x$$−$$1$$,$$0$$≤x≤$$2$$, then $$f($$|x|$$)$$ is defined as

Correct option is 3f(|x|)=−x−1,−2≤x≤0x−1,0<x≤2

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$Let f (x) be defined on [- 2, 2] and is given by f (x) = \{\begin{array}{cc} - 1, & - 2 \leq x \leq 0 \\ x - 1, & 0 \leq x \leq 2 \end{array}, then f (| x |) is defined as$

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f(|x|)=1−2≤x≤01−x,0

f(|x|)=x−1∀x∈R

f(|x|)=−x−1,−2≤x≤0x−1,0

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detailed solution

Correct option is C

We have f(x)=−1,−2≤x≤0x−1,0≤x≤2f(⌊x)=−1,−2≤|x|≤0|x|−1,0≤|x|≤2⇒ f(⌊x∣)=|x|−1, 0≤|x|≤2 (as −2≤|x|≤0 is not possible) ⇒ f(|x|)=−x−1,−2≤x≤0x−1,0

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Let f(x) be defined on [−2,2] and is given by f(x)=−1,−2≤x≤0x−1,0≤x≤2, then f(|x|) is defined as

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$Let f (x) be defined on [- 2, 2] and is given by f (x) = \{\begin{array}{cc} - 1, & - 2 \leq x \leq 0 \\ x - 1, & 0 \leq x \leq 2 \end{array}, then f (| x |) is defined as$