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

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

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

Answer

Explanation:

Step1: Recall tangent - domain property

The tangent function $y = \tan(t)$ is undefined when $t=(2n + 1)\frac{\pi}{2}$, where $n\in\mathbb{Z}$. For the function $y=\tan(\frac{x}{8})$, we set $\frac{x}{8}=(2n + 1)\frac{\pi}{2}$.

Step2: Solve for $x$

Multiply both sides of the equation $\frac{x}{8}=(2n + 1)\frac{\pi}{2}$ by 8. $x = 4(2n + 1)\pi=4\pi+8n\pi$, where $n\in\mathbb{Z}$.

Answer:

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