How to find the input that makes the function get a specific value

Hello, I have a function that represents the number of cycles of loading to a component, to grow a crack from length ai to af

N = @(ai,af)

I want to make another function that gives me the final length for a given number of cycles N and initial negth ai

Thanks

Answer 1

[Walter Roberson]

You could consider minimizing

@(AF) (N(GIVEN_AI,AF) - TARGET_N).^2

However, presumably "number of cycles" is an integer. If it tried two different AF and both of them returned the same N value that was not the target, then the minimizers would not have anything to go on about which direction to move. So you cannot use fminsearch() or fmincon() because thoe require continuous functions. You could probably try with ga() though.