How to "solve" a "function"

Lets take the "function" example from MATLAB website:

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Define a function in a file named average.m that accepts an input vector, calculates the average of the values, and returns a single result.

function y = average(x)

if ~isvector(x)

    error('Input must be a vector')

end

y = sum(x)/length(x);

end

Call the function from the command line.

z = 1:99;

average(z)

ans = 50

source: http://www.mathworks.co.uk/help/matlab/ref/function.html The first example.

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This function can give us the average. If we know the average, how could we use "solve" to find out the initial inputs?

[Tiancong]

Sorry, I think I didn't give a good example. Could you help me on my real problems pleases? Thank you so much! Here is the link:

http://www.mathworks.com/matlabcentral/answers/113156-how-to-find-implied-volatility-using-solve

Answer 1

[Amit]

The issue here is that you cannot reverse engineer this kind of function. If you know the average and lets say you know the size of the vector that gave the average, still can not determine the vector by any method or algorithm using any program in the world.

you can understand it like this: Lets say the average is 10 and size of vector is 2. then possible solutions will be [0 20],[9 11], [10 10] and many many many more. You can never figure out (unless you have some other information) which was the original vector that gave you the average of 10.

[Tiancong]

Sorry, I think I didn't give a good example. Could you help me on my real problems pleases? Thank you so much! Here is the link:

http://www.mathworks.com/matlabcentral/answers/113156-how-to-find-implied-volatility-using-solve

[Amit]

Answered there already.