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F(x) = ax+3, x>5
8 , x=5
x^2 + bx + a, x<5

Find a and b so that f(x) is continuous everywhere.

  • calculus -

    For x to be continuous everywhere,
    Lim x→5 =8 .....(1)
    Lim x→5- =8,.....(2), and
    Lim x→5+ =8,.....(3)

    (1) is satisfied by setting
    (2) can be satisfied by setting
    F(5)=ax+3 = 8
    and solving for a.
    (3) can be satisfied by setting
    F(5) = x^2 + bx + a = 8
    and solving for b using the previously solved value of a.

    Can you take it from here?

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