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Math Help - inverse function, solving for x with two variables

  1. #1
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    inverse function, solving for x with two variables

    Hello,

    I need to find the inverse function (finding f^-1) of f(x)= sqrt[3-x].

    So I figured y = sqrt[3-x]

    then solve for x to get x = 3- y^2 (?) when I graph it does not look like the inverse.

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  2. #2
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    What you did is half correct. You just have to switch the y and the x to get the inverse function.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Chop Suey View Post
    What you did is half correct. You just have to switch the y and the x to get the inverse function.
    Quote Originally Posted by 2clients View Post
    Hello,

    I need to find the inverse function (finding f^-1) of f(x)= sqrt[3-x].

    So I figured y = sqrt[3-x]

    then solve for x to get x = 3- y^2 (?) when I graph it does not look like the inverse.

    As Chops mentioned, just swap the x and y values of the function:

    y=\sqrt{3-x}\rightarrow x=\sqrt{3-y}

    Then solve for y to find f^{-1}(x).

    --Chris
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  4. #4
    o_O
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    Don't forget the restriction on the domain of the inverse: y = \sqrt{3-x} \geq 0 meaning that when you interchange x's and y's, then the 'new' x is greater than or equal to 0.
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