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Math Help - by finding inverse of the function, solve the equation

  1. #1
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    by finding inverse of the function, solve the equation

    I don't get how can we solve an equation by finding the inverse of that function. What has the inverse of that function got to do with solving the equation?

    Function is:

    f(x) = (x + 3) / (x -5)

    Equation is:

    (x+3) / (x-5) = 2

    Please help ...
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  2. #2
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    Quote Originally Posted by struck View Post
    I don't get how can we solve an equation by finding the inverse of that function. What has the inverse of that function got to do with solving the equation?

    Function is:

    f(x) = (x + 3) / (x -5)

    Equation is:

    (x+3) / (x-5) = 2

    Please help ...
    So you want to solve f(x) = 2.

    Apply the inverse function f^{-1} to both sides:

    f^{-1}(f(x)) = f^{-1}(2).

    But f^{-1}(f(x)) = x.

    Therefore x = f^{-1}(2).

    So the solution to \frac{x+3}{x-5} = 2 is x = f^{-1}(2).

    You know how to find the inverse of f(x) = \frac{x+3}{x-5} ? (No? This thread here might give you some clues ......)
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