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mtanti
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If I give you a function f(x) as a black box (you can't see the contents of it) and you can try any value of x you want and note the output values, would it be possible to find an identicle function of it?
mtanti said:If I give you a function f(x) as a black box (you can't see the contents of it) and you can try any value of x you want and note the output values, would it be possible to find an identicle function of it?
I think so. I mean no matter how the function looks like, we can always approximate it using Fourier series and write it as a sum of cos() and sin() terms.mtanti said:If I give you a function f(x) as a black box (you can't see the contents of it) and you can try any value of x you want and note the output values, would it be possible to find an identicle function of it?
robert Ihnot said:So, we would have no way to find this out, or even to express such numbers since they required an infinite number of decimals.
To determine a function with only knowing the input/output, you must first gather a set of input and output pairs. Then, you can plot these points on a graph and look for a pattern or trend. Once you have identified a pattern, you can use it to write an equation for the function.
If there is no obvious pattern, you may need to gather more input/output pairs or try using different methods to determine the function, such as using a table or creating a scatter plot. You may also need to consult with a math expert for assistance.
No, you need at least two input/output pairs to determine a function. This is because a function requires at least two points to create a line or curve.
To check if the function you have determined is correct, you can plug in the input values into the equation and see if it matches the corresponding output values. You can also graph the function and see if it fits the input/output pairs.
There are no shortcuts for determining a function with only input/output. However, it may be helpful to familiarize yourself with common functions and their corresponding graphs, such as linear, quadratic, and exponential functions. This can help you identify patterns more easily.