Transform a function in terms of y

[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

 

[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.

 

[Dick]

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.

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.

 

[sutupidmath]

It's a cubic, stupidmath. I wouldn't even try to solve it.

Damn...lol... i didn't notice that the last term was cubic at all... that's why alll my hints work for a quadratic equation... and yeah, solving cubic polynomials is painful as far as words go, sonce i haven't learned how to do it yet.

 

[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.