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1 August, 19:49

For what values of a and b is the following function is continuous at every x:

-7 x ≤ - 3

f (X) = ax-b - 3< x < 1

3 x ≥ 1

Find the values is a and b ix f (x) continuous at every x?

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  1. 1 August, 19:57
    0
    I have a solution here to the same problem but a slight different given:

    -1 x<=-1

    ax-b - 1
    2 x>=1

    The solution is as follows:

    f (x) = {-1, x ≤ - 1

    ... { ax - b, - 1 < x < 1

    ... { 2, x ≥ 1

    Then we must have:

    lim (x-->-1) - 1 = lim (x-->-1) ax - b

    ==> - 1 = - a - b

    ==> a + b = 1

    And we must have:

    lim (x-->1) ax - b = lim (x-->1) 2

    ==> a - b = 2

    So we need to solve the system of equations given by:

    a + b = 1

    a - b = 2

    After doing so, you should get that:

    a = 3/2

    b = - 1/2

    By studying the solution above, you now have the ability to answer the problem on your own!
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