question 38 (1 point) find the x - value (if any) at which f(x) is not continuous. f(x)=sin(2x)

Explanation:

Step1: Recall continuity definition

A function $y = f(x)$ is continuous at a point $x = a$ if $\lim_{x\rightarrow a}f(x)=f(a)$. The sine - function $y = \sin(u)$ is continuous for all real values of $u$.

Step2: Analyze the given function

For the function $f(x)=\sin(2x)$, let $u = 2x$. Since $u$ is a linear function of $x$ (continuous for all real $x$) and $y=\sin(u)$ is continuous for all real $u$, the composition $y = f(x)=\sin(2x)$ is continuous for all real $x$.

Answer:

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