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Find the inverse of f if f(x) = x^2 - 8x + 8 and x is less than or equal to 4

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Find [itex]f^{-1}(x)[/itex] if [itex]f(x)=x^{2}-8x+8[/itex] and [itex]x\leq4[/itex]

    3. The attempt at a solution
    I set [itex]y=x^{2}-8x+8[/itex], and then switch y and x to get [itex]x=y^{2}-8y+8[/itex].
    I then try solving for y, but I end up with y's on both sides of the equation:

    [itex]x=y^{2}-8y+8[/itex]

    [itex]x-8=y^{2}-8y[/itex]

    [itex]x-8=y(y-8)[/itex]

    [itex]\frac{x-8}{y-8}=y[/itex]

    [itex]???[/itex]
     
  2. jcsd
  3. Oct 18, 2011 #2

    CompuChip

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    It's a quadratic equation in y, so try the quadratic formula :-)
     
  4. Oct 18, 2011 #3

    SammyS

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    or complete the square.

    [itex]x-8=y^{2}-8y[/itex]

    [itex]x-8+16=y^{2}-8y+16[/itex]

    [itex]x+8=(y-4)^2[/itex]

       

    Don't forget the ± when taking the square root.

    The range of a function's inverse, f -1(x), is the same as the domain of the function, f(x).
     
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