determine the intervals on which the function f(x) = 4 / (x^2 - 25) is continuous. choose the correct answer…

Explanation:

Step1: Find the domain - undefined points

A rational function $\frac{4}{x^{2}-25}$ is undefined when the denominator is 0. Set $x^{2}-25 = 0$. We know that $x^{2}-25=(x + 5)(x - 5)=0$. Solving $(x + 5)(x - 5)=0$ gives $x=-5$ or $x = 5$.

Step2: Determine the continuity intervals

A rational function is continuous everywhere in its domain. The domain of $f(x)=\frac{4}{x^{2}-25}$ is all real - numbers except $x=-5$ and $x = 5$. So the function is continuous on the intervals $(-\infty,-5),(-5,5),(5,\infty)$.

Answer:

A. $(-\infty,-5),(-5,5),(5,\infty)$