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Let f(x)={{:(ax" ,",,x lt 2),(ax^(2...

Let `f(x)={{:(ax" ,",,x lt 2),(ax^(2)+bx+3",",,x ge 2):}`
If f is differentiable for all x, then value of (a, b) is equal to

A

`(1,2)`

B

`((3)/(2),(9)/(2))`

C

`((3)/(4),-(9)/(2))`

D

`((3)/(4),-(9)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • Let f(x)={{:(Ax,,","x lt 1),(Ax^(2)+Bx+4,,","x ge 1):} If f is differentiable for all x, then

    A
    `A=2,B=-2`
    B
    `A=-4,B=4`
    C
    `A=1,B=-1`
    D
    `A=4,B=-4`

  • If the function f:R to R defined by f(x)={{:(ax,,x lt 2),(ax^(2)-bx+3,,x ge2):} is differentiable, then the value of f'(-3)+f'(3) is equal to

    A
    0
    B
    3
    C
    4
    D
    `(15)/(2)`

  • Let f(x)={{:(x^(3)-1",", x lt2),(x^(2)+3"," , x ge 2):} Then

    A
    `f^(-1)(x)={{:((x+1)^(1//3)",", x lt2),((x-3)^(1//2)+"," , x ge 2):}`
    B
    `f^(-1)(x)={{:((x+1)^(1//3)",", x lt 7),((x-3)^(1//2)+"," , x ge 7):}`
    C
    `f^(-1)(x)={{:((x+1)^(1//3)",", x lt 1),((x-3)^(1//2)+"," , x ge 7):}`
    D
    `f^(-1)(x)` does not exist

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