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Let f(x) be defined on [-2, 2] and be gi...

Let `f(x)` be defined on `[-2, 2]` and be given by `f(x)= {:{(-1,-2 le x le0),(x-1,0 lt 2 le 2):}` and `g(x)=f(|x|)+|f(x)|`, Then find `g(x)`

A

`g(x)={:{(-x,-2 le x le 0),(0,0 lt x le 1),(2(1-x),1 lt x le 2):}`

B

`g(x)={:{(-x,-2 le x le 0),(0,0 lt x le 1),(2(x-1),1 lt x le 2):}`

C

`g(x)={:{(x,-2 le x le 0),(0,0 lt x le 1),(2(x-1),1 lt x le 2):}`

D

`g(x)={:{(x,-2 lex le 0),(1,0 lt x le 1),(2(x-1), 1 lt x le 2):}`

Text Solution

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The correct Answer is:
B
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