the point (a, b) is the point of intersection of the graphs of y = f(x) and y = g(x). complete the paragraph…

Explanation:

Step1: Recall point - function relationship

If a point $(a,b)$ lies on the graph of $y = f(x)$, then $b=f(a)$ because for the function $y = f(x)$, when $x = a$, the corresponding $y$-value is $b$.

Step2: Apply to second function

If a point $(a,b)$ lies on the graph of $y = g(x)$, then $b = g(a)$ since for the function $y = g(x)$, when $x=a$, the $y$-value is $b$.

Step3: Equate the two expressions

Since $b=f(a)$ and $b = g(a)$, we have $f(a)=g(a)$.

Step4: Identify the solution

The $x$-coordinate of the point $(a,b)$ (which is $a$) must be a solution of the equation $f(x)=g(x)$ because when $x = a$, $f(x)$ and $g(x)$ are equal.

Answer:

The point $(a,b)$ lies on the graph of $y = f(x)$, so $b = f(a)$. The point $(a,b)$ also lies on the graph of $y = g(x)$, so $b = g(a)$. This means that $f(a)=g(a)$. So, the $x$-coordinate of the point $(a,b)$ must be a solution of the equation $f(x)=g(x)$.