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Consider the function f(x)=f(x)={{:(x-1"...

Consider the function `f(x)=f(x)={{:(x-1",",-1lexle0),(x^(2)",", 0lexle1):}`
and`" "g(x)=sinx.`
If `h_(1)(x)=f(|g(x)|)`
`" and "h_(2)(x)=|f(g(x))|.`
Which of the following is not true about `h_(1)(x)`?

A

h(x) is continuous for `x in [-1, 1]`

B

h(x) is differentiable for `x in [-1, 1]`

C

h(x) is differentiable for `x in [-1, 1] - {0}`

D

h(x) is differentiable for `x in (-1, `)-{0}`

Text Solution

Verified by Experts

The correct Answer is:
C
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