Find the input values of a function within an output range.

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Let us say we have a funtion like y= @(n) f(n).
How would you find the range of n values for the y range y[ ymin,ymax] is there some sort of inverse function command in MATLAB with which you could do this? I.E. n=@(y) f^(-1)(y) or something similar.
A practical example would be:
Rend = @(n) Pu(n)/Pa(n); % Where Pu(n) and Pa(n) are other functions which also depend of n.
% Find value range of n for Rend==[R1,R2] where R1 is the min of the range
% and R2 the max of the range.
Thanks in advance.

Accepted Answer

Joel Lynch
Joel Lynch on 9 Jun 2021
Edited: Joel Lynch on 9 Jun 2021
If you cannot solve algebraically (no closed form solution), then fzero is the best bet. Something like this:
% example y range
y = linspace(ymin,ymax);
% Create empty array of n values of same size
nsol = zeros(size(y));
% Loop y values
for i=1:numel(y)
% grab local y
ylocal = y(i);
% Setup fzero function function
myfunc = @(n) Pu(n)/Pa(n) - ylocal;
% Solve for myfunc=0
nsol(i) = fzero( myfunc, nguess );
Note that "fzero" is being adapted from solving for 0, to solving for ylocal by subtracting that term. There are probably faster ways to get "myfunc" defined outside the loop.
  1 Comment
Nigel Brauser
Nigel Brauser on 4 Nov 2022
Thank you very much, this was very helpful. Particularly your simple handling of subtracting ylocal to find the desired value, rather than just 0.

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