Solve Trendline Equation for X

**bpitta** · 10-12-2009, 09:45 PM

I have a trendline that fits a 4th order polynomial perfect. Excel gives the trendline as a y= format. I want to solve the equation to get an X= format so I can use the relationship to tell me values of X.

Does anyone know how to do this?

**shg** · 10-12-2009, 11:32 PM

For a polynomial other than linear, there are, in general, multiple values of y for any given x; i.e., the inverse of a polynomial is not a function.

For a simple example, consider y =x^2.

**zbor** · 10-13-2009, 02:10 AM

Inverse of polynomial function is a function.
Thou, solutions can be real or complex and ambiguous.

**shg** · 10-13-2009, 10:34 AM

Originally Posted by http://en.wikipedia.org/wiki/Function_(mathematics)

In mathematics a function is a relation between a given set of elements (the domain) and another set of elements (the codomain), which associates each element in the domain with exactly one element in the codomain.

The inverse of most second-order or higher polynomial are multi-valued, and therefore, by definition, not functions.

**zbor** · 10-13-2009, 05:21 PM

Or a function that is called non-injective function

**shg** · 10-13-2009, 05:39 PM

To say a function is injective is to say it is strictly monotone. y=2x is injective. y=x^3 is injective (and so is it's inverse). y=x^2, and polynomials of degree greater than 1 in general, are not injective.

Polynomial inverses, in general, aren't non-injective functions; they aren't functions at all.