Question

Why the x-coordinate of the point of intersection is a solution to the equation f(x) = g(x)?

Answer 1

If 2 graphs meet at the same point means that for the same x both function give the same outcome/value y. That's why they are equal. Suppose f(x) = x^2 -1 and g(x) = 2x-1. This function meet at the point x=2(the point of intersection). Let's put the value of intersection in the functions. f=2^2-1=3, g= 2*2-1=3, we proved in another way why that's the point where 2 graphs are equal each other.