algebra II

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How do you verify inverses?
the question is y=3x-3...
we know how to make an inverse but how do you verify it using composition?

  • algebra II -

    one way is to check to make sure that

    f(f -1(x)) = x
    and
    f -1(f(x)) = x

    For example, if

    f(x) = 2x-7
    then solve for x to get f -1
    y = 2x-7
    (y+7)/2 = x
    so, f -1(x) = (x+7)/2

    Now,

    f -1(f(x)) = (f(x)+7)/2
    = ((2x-7)+7)/2
    = (2x)/2
    = x

    and
    f(f -1(x)) = 2f -1(x) - 7
    = 2*(x+7)/2 - 7
    = x+7-7
    = x

    Using values, just plug 'em in:

    f(3) = 6-7 = -1
    f -1(-1) = (-1+7)/2 = 3

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