f(0)=f(0)f(0)= 1

Then f(0)= 1.

Suppose f(x)=0, then f(0)=f(x)f(-x)=0.

So f (x) < > 0

So the range of f(x) is a positive integer.

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Summary: Exponential function is a special case of this function, but it cannot be said that this function must be an exponential function.

However, starting with some properties of exponential function, it is found that the solution of this function should conform to the mathematical thinking mode of "from special to general".