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Math Help - Inverse function

  1. #1
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    Question Inverse function

    Find the inverse of f(x)=7x informally.
    Verify that f(f^-1(x))=x and f^-1(f(x))=x.

    First of all, what is meant by informally???
    Then, after I find the inverse informally, what do I do?
    Please and Thank You's
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  2. #2
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    Quote Originally Posted by iheartthemusic29 View Post
    Find the inverse of f(x)=7x informally.
    Verify that f(f^-1(x))=x and f^-1(f(x))=x.

    First of all, what is meant by informally???
    Then, after I find the inverse informally, what do I do?
    Please and Thank You's
    As there isn't much to do to find it analytically, I suppose they mean guess at it?

    Anyway, to find the inverse of a function f(x) use the following steps:
    1) Set y = f(x)
    2) Now let x = f(y) (This amounts to reflecting the graph over the line y = x, which graphically gives the inverse function.)
    3) Solve for y. We'll have y = g(x) as the solution. g(x) is the inverse to f(x).

    In this case:
    1) Let y = f(x) = 7x
    2) Let x = 7y
    3) y = (1/7)x <-- This is the inverse function, f^{-1}(x) = \frac{x}{7}.

    To prove this we need to show that f(f^{-1}(x)) = f^{-1}(f(x)) = x

    So
    f(f^{-1}(x)) = f \left ( \frac{x}{7} \right ) = 7 \left ( \frac{x}{7} \right ) = x (Check!)

    f^{-1}(f(x)) = f^{-1}(7x) = \frac{(7x)}{7} = x (Check!)

    -Dan
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  3. #3
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    Talking

    Thanks! That's the way I found the inverse, too, but I wasn't sure if that was considered "informal".
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