Question

determine where the function f(x) = \frac{2x}{x^{2}+25} is continuous. the function is continuous on . (simplify your answer. type your answer in interval notation.)

Explanation:

Step1: Recall continuity condition

A rational function $\frac{f(x)}{g(x)}$ is continuous where $g(x)
eq0$. Here $f(x) = 2x$ and $g(x)=x^{2}+25$.

Step2: Find when denominator is zero

Set $g(x)=x^{2}+25 = 0$. Then $x^{2}=- 25$. Since the square of a real - number $x\in R$ is non - negative ($x^{2}\geq0$ for all real $x$), there are no real solutions for $x$ such that $x^{2}=-25$.

Answer:

$(-\infty,\infty)$