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

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Edward Simpson Songel on 9 Jun 2021
Edited: Joel Lynch on 9 Jun 2021
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.

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 );
end
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.