Statistics

hint: type of growth for f(x) is linear, quadratic, exponential, logarithmic? etc.
beyond that....
do your own damn homework.

I am not a mathematician: Hence the question. The question was not on any homework.

Ok, from a mathematics standpoint, you need to find what category of function bounds your functions. for example, f(x)=n^x (exponential growth) grows much faster than f(x)=x^n (quadratic growth) given n is a constant. The question as to whether f(x) and h(x) are significantly different depends less on extremely large values of x and more on large changes in x.
the mathematical proofs for this can be proven for given functions by repeatedly taking their derivitaves and seeing which results in a constant first.
In the case where both functions are bound by the same generic function, for example f(x)=x^2 and h(x)=x^2+x+1 are both bound by a generic equation g(x)=ax^2+bx+c, significant differences apply more to smaller changes in x. in this case, you want to do a variance analysis over a specified range of x, or simply subtract the functions from each other. In the case of f(x) and h(x) above, the result is a linear equation which I would define as insignificantly different, or a high slope linear equation that one could interpret as significantly different.

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