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Let f(x) = x cos^(-1)(sin-|x|), x in (-...

Let `f(x) = x cos^(-1)(sin-|x|)`, `x in (-pi/2,pi/2)`

A

`f(0) = - pi/2`

B

f'(x) is not defined at x = 0

C

f'(x) is increasing in `( -pi/2, 0)` and f'(x) is decreasing in `(0, pi/2)`

D

f'(x) is decreasing in `( -pi/2, 0)` and f'(x) is increasing in `(0, pi/2)`

Text Solution

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The correct Answer is:
D
NA
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Knowledge Check

  • Let f(x)=|x|+|sin x|, x in (-pi//2,pi//2). Then, f is

    A
    nowhere continuous
    B
    continuous and differentiable everywhere
    C
    nowhere differentiable
    D
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    `f((8 pi)/(9))= e^((5pi)/(18))`
    B
    `f((8pi)/(9))= e^((13pi)/(18))`
    C
    `f(-(7pi)/(4))=e^((pi)/(12))`
    D
    `f(-(7pi)/(4))=e^((11pi)/(12))`

  • Let f(x) = sin^(-1) x + cos^(-1) x ". Then " pi/2 is equal to

    A
    `f(- 1/2)`
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    `f(k^(2) - 2k + 3), k in R`
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