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If f(x)={(x-4)/(|x-4|)+a ,\ \ \ if\ x<4a...

If `f(x)={(x-4)/(|x-4|)+a ,\ \ \ if\ x<4a+b ,\ \ \ if\ x=4(x-4)/(|x-4|)+b ,\ \ \ if\ x >4` is continuous at `x=4` , find `a ,\ b` .

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To solve the problem, we need to ensure that the function \( f(x) \) is continuous at \( x = 4 \). This means that the left-hand limit as \( x \) approaches 4, the value of the function at \( x = 4 \), and the right-hand limit as \( x \) approaches 4 must all be equal. Given the function: \[ f(x) = \begin{cases} \frac{x-4}{|x-4|} + a & \text{if } x < 4 \\ a + b & \text{if } x = 4 \\ ...
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Knowledge Check

  • Let f(x) ={{:((x-4)/(|x-4|)+a, x lt 4),((x-4)/(|x-40|)+b, x gt 4):} , Then f(x) is continuous at x = 4, when

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

  • The values of a and b such that the function f defined by f(x) = {{:((x-4)/(x-4)+a , if x lt 4),(a+b, if x=4),((x-4)/(|x-4|)+b, if x gt 4):} is continuous function at x = 4 are

    A
    a = 1and b = −1
    B
    a = −1and b = 1
    C
    a = 0 and b = − 1
    D
    a = 1 and b = 0

  • If f(x) = (sin [ 4(x-3)])/(x^(2)-9) , x != 3, is continuous at x = 3 then f(3) = ….

    A
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    C
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    D
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