If `f(x)={{:(,4,-3lt x lt -1),(,5+x,-1le x lt 0),(,5-x,0 le x lt 2),(,x^(2)+x-3,2 lt x lt 3):}` then, f(|x|) is

Options

A. differentiable but not continuous in (-3,3)
B. continuous but not differentiable in (-3,3)
C. continuous as well as differentiable in (-3,3)
D. neither continuous nor differentiable (-3,3)

Answer

B

Explanation

We have
`{{:(,4,-3 lt x lt -1),(,5+x,-1 le x lt 0),(,5-x,0 le x lt 2),(,x^(2)+x-3,2 le x lt 3):}`
`therefore f(|x|)={{:(,5-|x|,"if "0 le |x| lt 2),(,|x|^(2)+|x|-3,"if "2 le |x| lt 3):}`
`Rightarrow f(|x|)={{:(,5+x,"if "-2 lt x lt 0),(,5-x,"if "0 le x lt 2),(,x^(2)-x-3,"if "-3 lt x le-2),(,x^(2)+x-3!,"if "2 le x lt 3):}`
Clearly, f(x) is continuous in (-3,3). But, it is not differenitable at x=0, -2,2. Hence, f|x| is continuous but not differentiable in (-3,3)