Explain why f(x) = x−4 is not the identical function of g(x) = x^2 −7x + 12/ x−3

Answer 1

Hi. It may seem a little confusing at first because if you do long division, you get the same function as f(x). But the trick is that we cannot necessarily perform long division because there is a case where (x-3) is zero. That is the case when x=3.

So when we graph g(x), we notice something interesting. The point on the graph corresponding to x=3 is undefined because division by zero is undefined.

However, f(x) has a point that is defined at x=3; therefore, f(x) is different or not identical to g(x).

Hope that helps!