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The set of all points where the function...

The set of all points where the function `f(x)=sqrt(1-e^(-x^2))` is differentiable is

A

`(0,oo)`

B

`(-oo,oo)`

C

`(-oo,0)uu(0,oo)`

D

`(-1,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=sqrt(1-e^(-x^(2)))`
`f'(x)=(1)/(2sqrt(1-e^(-x^(2)))).(-e^(-x^(2)))(-2x)`
`f'(x)=(xe^(-x^(2)))/(sqrt(1-e^(-x^(2))))`
f'(x) is defined for all values of x, except 0.
`:.f(x)` is differentiable on `(-oo,0)cup(0,oo)`
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