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f(x)={(5, xle1),(a+bx,1<x<,3),(b+5x,3lex...

`f(x)={(5, xle1),(a+bx,1

A

continuous if a =5 and b = 5

B

continuous if a =-5 and b = 10

C

continuous if a = 0 and b = 5

D

not continuous for any values of a and b

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Let f:RtoR be a function defined as f(x)={(5,"if", xle1),(a+bx,"if", 1ltxlt3),(b+5x,"if",3lexlt3),(30,"if",xge5):} Then f is :

    A
    continuous if `a=-5` and b=10
    B
    continuous if `a=0` and `b=5`
    C
    not continuous for nay value of a and b
    D
    continuous if a=5 and b=5

  • If f(x)={(x","xle1,),(x^2+bx+c",",xgt1):} then find the values of b and c if f(x) is diferentiable at x=1.

    A
    b=c=1
    B
    b=-1,c=1
    C
    b=0,c=1
    D
    b=-1,c=0

  • If f(x)={(x^(2),xle1),(1-x,xgt1):} & composite function h(x)=|f(x)|+f(x+2) , then

    A
    `h(x)=2x^(2)+4x+4 AAxle-1`
    B
    `h(x)=x^(2)+x+1 AA-1ltxle1`
    C
    `h(x)=x^(2)-x-1 AA-1ltxle1`
    D
    `h(x)=-2AAxgt1`

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    If f(x)={(ax+3, xle2),(a^2x-1, xgt2):} , then the values of a for which f is continuous for all x are

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    If f : IR rarr IR be defined by f(x)={(2x,xgt3),(x^(2),1ltxle3."thenf(-1)+f(2)+f(5)=),(3x,xle1):}

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