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If f(x)= int(0)^(x)(f(t))^(2) dt, f:R ra...

If `f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R ` be differentiable function and `f(g(x))` is differentiable at `x=a`, then

A

g(x) must be differentiable at x = a

B

g(x) is discontinuous, then f(a) = 0

C

`f(a) ne 0`, then g(x) must be differentiable

D

None of these

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The correct Answer is:
B, C
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  17. Which of the following functions is differentiable at x = 0? cos (|x|...

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  19. If the function g(x)={{:(,k sqrt(x+1),0 le x le3),(,mx+2,3lt xle5):...

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