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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f(|x|)=1−2≤x≤01−x,0

f(|x|)=x−1∀x∈R

f(|x|)=−x−1,−2≤x≤0x−1,0

none of these

answer is C.

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Detailed Solution

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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