The functions f and h are defined as follows:
f(x) = (x + 5)/(x - 7) and h(x) = (x + 5)(x - 7).
Explain why the functions f and h are not the same function.
We can use proof by contradiction here
We can first assume first that they are the same function, which means that for every single x value there is the same y value. It is easy to see that is not the case here, for example if f(5) is -5, while h(5) is -20. Because of this, that means the statement we assumed at the beginning must be false, so they are not the same function.