Symbolic Toolbox: transforming a function y(x) to x(y)

Question

回答： Ghada Saleh 2015-7-17

Hello everyone,

I have a function y(x) an need to find x(y) for x>=0.

y(x) is in the form: y(x) = a4*x^4 + a3*x^3 + a1*x

Where a4, a3, and a1 are real factors.

Is it possible to do this with Matlab's Symbolic Toolbox?

Thanks in advance, Marco R.

Answer 1

Ghada Saleh 2015-7-17

Hi Marco,

You can inverse your function using functional inverse in Symbolic Math Toolbox. You can also add the constraint as an assumption on 'x'.

The following piece of code might be helpful:

 >> syms x a1 a3 a4;
 >> assume(x >= 0);
 >> y = a4*x^4 + a3*x^3 + a1*x;
 >> g = finverse(y, x)

Note that MATLAB will represent the output in terms of 'x' which should represent 'y' in your case. To illustrate, refer to the following example:

>> syms x
>> f(x) = 1/tan(x);
>> g = finverse(f)

g(x) = atan(1/x)

I hope this helps,

Ghada