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Let f (x) = {{:(min (x"," x ^(2)), x ge...

Let `f (x) = {{:(min (x"," x ^(2)), x ge 0),( max (2x "," x-1), x lt 0):},` then which of the following is not true ?

A

f (x) is not differentiable at `x=0`

B

f (x) is not differentiable are exactly two points

C

f (x) is continous everywhere

D

f (x) is strictly increasing `AA x in R`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Let f(x) ={{:(min{x,x^(2)},x le 0), (max {2x","x^(2)-1},xlt0):} then which of the following is not true ?

    A
    f(x) is continuous at x=0
    B
    f(x) is not differentiable at x=1
    C
    f(x) is not differentiable at exactly three points
    D
    none of these

  • If f(x) = {(x,",", x ge 0),(x^(2),",",x lt 0):} , then f(x) is

    A
    continuous on R
    B
    discontinuous on R
    C
    continuous on R except at x =0
    D
    discontinuous on R except at x = 0

  • Let [x] = greatest integer le x and {x} =x - [x] , Let, f_(1)(x) = 2/pi [sin^(-1) (x) + cos^(-1)(x)] f_(2)(x) = sin^(2) (log_(5)x) + cos^(2) (log_(3)x) f_(3)(x) = sgn({x} +1) and f_(4)(x) = sec^(2) [{x}] - tan^(2) {[x]} sgn(x) = {{:(-1, if x lt 0),(0, if x=0),(1, if gt 0):} Then which of the follwing is not true?

    A
    `f_(1) =f_(2)`
    B
    `f_(1) = f_(3)`
    C
    `f_(1) = f_(4)`
    D
    `f_(3) = f_(4)`

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