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Math Help - When A Function Is to the power of -1

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    When A Function Is to the power of -1

    When A Function Is to the power of -1what does it mean?
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  2. #2
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    Quote Originally Posted by abc10 View Post
    When A Function Is to the power of -1what does it mean?
    It can have two meanings.

    If you take the literal meaning for "power of -1", then

    f^{-1}(x) = \frac{1}{f(x)}.


    But the more-often used meaning for this notation is the "Inverse Function"

    Basically, if you have a function f(x), then the inverse function f^{-1}(x) is the function whose graph is a reflection along the line y = x. So the x and y values have swapped. Also, the domain and range have also swapped.
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    Expanding slightly on what prove it said.

    A function to the power one -1 is the inverse of that function.

    the inverse of a number is a number that multiplied by the original equals 1.
    x^{-1}x=1 always.


    ----- \int
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  4. #4
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    Inverse of a function

    Hello abc10

    Just to expand a little further on the replies so far:

    Yes, f^{-1} denotes the inverse of the function f.

    Let's take a simple function like f(x) = 2x + 5. Then, for example:
    f(0) = 5

    f(1)=7

    f(2)=9

    ... and so on.
    Then f^{-1} is the function that reverses this process. So:
    f^{-1}(5) = 0

    f^{-1}(7)=1

    f^{-1}(9) = 2

    ... and so on.
    Perhaps you can work out what f^{-1} does? Since f multiplies by 2 and then adds 5, f^{-1} will do the 'opposite' things in the reverse order. In other words, f^{-1} will:

    • subtract 5; and then


    • divide by 2.

    So:
    f^{-1}(x)= \frac{x-5}{2}
    (Try this function with the values 5, 7 and 9 and check that you get 0, 1 and 2.)

    Grandad
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