question 40 (1 point) find the x - value (if any) at which f(x) is not continuous. f(x)=(x + 9)/(x^2 + 9)

Explanation:

Step1: Recall continuity condition

A rational - function $y = \frac{g(x)}{h(x)}$ is discontinuous where $h(x)=0$. Here, $g(x)=x + 9$ and $h(x)=x^{2}+9$.

Step2: Solve $h(x) = 0$

Set $x^{2}+9 = 0$. Then $x^{2}=-9$.

Step3: Analyze the solutions

In the real - number system, the square of a real number $x$ (i.e., $x^{2}$) is non - negative for all real $x$. So, the equation $x^{2}=-9$ has no real solutions.

Answer:

There are no real x - values for which $f(x)$ is not continuous.