# Transform a function in terms of y

1. Sep 9, 2008

### Fiorella

In a calculus problem i'm doing I have to transform f(x) = 4x^2 - x^3 and y = 18 - 3x in terms of y.

I did the second one and it's:

x = - (y - 18) / 3

But I can't transform the first one in terms of y

2. Sep 9, 2008

### sutupidmath

You mean to find its inverse, right? But notice that since your first function is a quadratic one, it means that it does not have an inverse on its whole domain, since the quadratic functions are not one-to-one, so they don't have inverses. But you can work it out in two separate procedures, first saying that x is greater or equal to 0, and the secon one saying that x<0. Now this way our function is one-to-one in the restriction domains, so we can find its inverses by simply switching coordinates, that is x's and y's.

3. Sep 9, 2008

### Dick

It's a cubic, stupidmath. I wouldn't even try to solve it. Fiorella, if this is about that tangent problem you've posted in multiple copies, you don't need to invert the functions.

4. Sep 9, 2008

5. Sep 9, 2008

### Dick

If you learn how to do it, try and forget it as fast as you can. There is a solution, but it's amazingly useless in practical problems.