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Thread: function defined

  1. #1
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    Question function defined

    For the function defined by f(x)=5x-4, find a formula for f^-1(x). My answer is f^-1(x)= 1 divided by 5x-4, is this right. thanks for checking.
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  2. #2
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    $\displaystyle f^{-1}(x)$ doesn't mean $\displaystyle \frac{1}{f(x)}$.

    Think of it this way:
    If $\displaystyle y = f(x) = 5x-4$ then the inverse function is denoted $\displaystyle f^{-1}(x)$ and is just the expression with the x and y switched, and then solved for y.

    Switching y and x, you get:

    $\displaystyle x = 5y - 4$.

    Isolate the y to get:

    $\displaystyle y = \frac{x+4}{5}$

    So $\displaystyle f^{-1}(x) = \frac{x+4}{5} = \frac{1}{5}x + \frac{4}{5}$.
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  3. #3
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    Smile answer

    I see now where I was wrong. thanks for checking my answer.
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