Is there a simpler solution for finding the inverse of a cubic function?

  • Thread starter Thread starter agricola
  • Start date Start date
  • Tags Tags
    Inverse
AI Thread Summary
Finding the inverse of a cubic function, represented as p=ax^3+bX^2+cX, is challenging due to its complexity. While the function can be positive monotonic under certain parameter conditions, it does not guarantee an analytic solution for the inverse. The general formula for cubic equations exists but is notably complicated, making practical application difficult. Numeric values can be plotted to visualize the function's behavior, which typically shows a tilted S shape. Ultimately, a simpler solution for finding the inverse remains elusive.
agricola
1
0
p=ax^3+bX^2+cX is positive monotonic and has an inverse X=G(p)

But I can't invert it. Is there an analytic solution?
For given parameter values I can plot numeric values- it has a tilted S shape.
 
Mathematics news on Phys.org
This is, by the way, a "cubic" equation, not "quartic". I take it, you mean by "is positive monotonic" that you are assuming values of a, b, and c such that the function is monotonic. Of course a cubic equation cannot always be positive. A true "quartic" (fourth degree) equation can but it cannot be monotonic.

There is a general formula for solutions to cubic equations that could, theoretically, give an inverse function for this, but it is extremely complicated.
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

B Are Inverse Problems More Complex Than Direct Problems in Mathematics?
Replies
13
Views
3K
I Can an inverse function of a special cubic function be found?
Replies
15
Views
2K
I Calculating the inverse of a function involving the error function
Replies
3
Views
2K
I Quadratic, cubic, quartic, quintic equations
Replies
16
Views
4K
MHB Finding Min Value of $\dfrac{|b|+|c|}{a}$ from Roots of Cubic Equations
Replies
4
Views
1K
MHB Understanding Cubic Equation Formula for Polynomials of Degree Three
Replies
9
Views
3K
MHB Max Value of $b$ for Real Roots of $f(x)$ and $g(x)$
Replies
2
Views
1K
I Get the time axis right in an inverse Fast Fourier Transform
Replies
2
Views
3K
MHB How can I find the inverse function for a given approximation?
Replies
3
Views
3K
Problem of solving the cubic function
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top