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Simple question on functions.

  1. Aug 17, 2011 #1
    I just need help turning a function of x into a function of y.

    I'll give you an example and maybe you can explain it and expand upon the idea.

    Thanks in advance.

    y = x^2 -5x (see a very simple function! I just can't figure out how to convert it).

    or y = x^2 - 2x
     
  2. jcsd
  3. Aug 17, 2011 #2

    Mark44

    Staff: Mentor

    What you're asking is not clear, but I think you are talking about finding the inverse function. In your first example, y = f(x) = x2 - 5x. Here y is a function of x. It is not, however, a one-to-one function, so the inverse will not be a function.

    To solve for x in terms of y, complete the square.
    y = x2 - 5x
    ==> y = x2 - 5x + (5/2)2 - (5/2)2 = (x - 5/2)2 - (5/2)2

    Can you take it from there?

    To make the inverse a function, restrict the domain of the original function to make it one-to-one.
     
  4. Aug 17, 2011 #3

    dynamicsolo

    User Avatar
    Homework Helper

    Beware, however: your function y = x2 - 5x (the graph of which is a parabola) assigns two different values of x to the same value of y . So when you "invert" this to get x = "something" , you will get a plus-or-minus sign, which tells us that we get back two functions of y , each corresponding to half of the original parabola.

    This is always a problem with even powers of x in a function; reversing the direction to return from y to x gives two possible values of x which could have led to that value of y , and a "rule" which assigns one value of y to two values of x is NOT a function. That's why we need to split your result into two parts. (We don't have this problem with odd powers of x .)
     
  5. Aug 18, 2011 #4
    Thank you for your answers.
    Yes I was looking to complete the square, and now that I've seen this it is quite a bit more complicated then I expected.
     
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