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If f(x) = {sinx , x lt 0 and cosx-|x-1...

If `f(x) = {sinx , x lt 0 and cosx-|x-1| , x leq 0` then `g(x) = f(|x|)` is non-differentiable for

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In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where g (x) =f (|x|) is non-differentiable.

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Knowledge Check

  • If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x gt 0, f(x) may be

    A
    `x^(2)`
    B
    x
    C
    `-x`
    D
    `-x^(3//2)`

  • If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0 then for xgt 0 , f(x) may be

    A
    `x^2`
    B
    x
    C
    `-x`
    D
    `-x^(3)`

  • Let f(x) = sinx + cosx, g(x) =x^(2)-1 . Then g(f(x)) is invertible for x in

    A
    `[-pi/2,0]`
    B
    `[-pi/2,pi]`
    C
    `[-pi/4,pi/4]`
    D
    `[0,pi/2]`

    • Similar Questions

    Explore conceptually related problems

    If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x gt 0, f(x) may be

    If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x gt 0, f(x) may be

    If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x gt 0, f(x) may be

    If function defined by f(x) ={(x-m)/(|x-m|) , x leq 0 and 2x^2+3ax+b , 0 lt x lt 1 and m^2x+b-2 , x leq 1 , is continuous and differentiable everywhere ,

    If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

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