what is the domain of the function $y = \tanleft(\frac{x}{8}\right)$?\nall real numbers except $4pi + 4npi$…

what is the domain of the function $y = \tanleft(\frac{x}{8}\right)$?\nall real numbers except $4pi + 4npi$, where $n$ is any integer\nall real numbers except $4pi+8npi$, where $n$ is any integer\nall real numbers except $8pi + 4npi$, where $n$ is any integer\nall real numbers except $8pi+8npi$, where $n$ is any integer

what is the domain of the function $y = \tanleft(\frac{x}{8}\right)$?\nall real numbers except $4pi + 4npi$, where $n$ is any integer\nall real numbers except $4pi+8npi$, where $n$ is any integer\nall real numbers except $8pi + 4npi$, where $n$ is any integer\nall real numbers except $8pi+8npi$, where $n$ is any integer

Answer

Explanation:

Step1: Recall tangent function domain

The tangent function $y = \tan(t)$ is undefined when $t=\frac{\pi}{2}+k\pi$, where $k\in\mathbb{Z}$.

Step2: Set the argument of given tangent equal to undefined - values

For $y = \tan(\frac{x}{8})$, we set $\frac{x}{8}=\frac{\pi}{2}+n\pi$, where $n\in\mathbb{Z}$.

Step3: Solve for $x$

Multiply both sides of $\frac{x}{8}=\frac{\pi}{2}+n\pi$ by 8. We get $x = 4\pi+8n\pi$, $n\in\mathbb{Z}$.

Answer:

all real numbers except $4\pi + 8n\pi$, where $n$ is any integer