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Let f(x) = {(x^(2)-a, if x lt 3),(bsqrt(...

Let `f(x) = {(x^(2)-a, if x lt 3),(bsqrt(x-2)+a, if 3 le x lt 6),(2x+b, if x ge 6):}` If f(x) is continuous `AA x in R` then the value of f(1)+f(3)+f(7), is

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f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3):}

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Knowledge Check

  • If f(x) {:(=x^(2)-1", if "x lt 3 ),(= 2ax ", if "x le 3 ) :} is continuous at x = 3 , then a = ……

    A
    `4/3`
    B
    `3/4`
    C
    `(-3)/4`
    D
    `(-4)/3`

  • f(x)={(|x|+3",","if", x le -3),(-2x",", "if", -3 lt x lt 3),(6x+2",","if",x ge 3):} is

    A
    continuous at x = -3 and discontinuous at x = 3
    B
    continuous at x = -3, 3
    C
    discontinuous at x = -3, 3
    D
    continuous at x = 3 and discontinuous at x = -3

  • Let f(x)={{:(ax-b,","x le 1),(3x,"," 1 lt x lt 2),(bx^2-a,"," x ge 2):} If f is continuous function then (a,b) is equal to

    A
    (1,2)
    B
    (1,3)
    C
    (3,6)
    D
    (6,3)

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

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