Using it's concept, it is found that the domain of the function y = tan(x/8) is given by:
All real numbers except [tex]x \neq 4\pi + 8n\pi[/tex], where n is any integer.
What is the domain of a function?
It is the set that contains all possible input values for the function.
Tangent of an angle is sine of the angle divided by the cosine of the angle, and the cosine is 0 at:
[tex]\frac{\pi}{2} + n\pi[/tex]
Hence, supposing a composite tangent function [tex]\tan{[f(x)]}[/tex], the domain is given by:
[tex]f(x) \neq \frac{\pi}{2} + n\pi[/tex]
In this problem, we have that [tex]f(x) = \frac{x}{8}[/tex], hence the domain is:
[tex]\frac{x}{8} \neq \frac{\pi}{2} + n\pi[/tex]
[tex]x \neq 4\pi + 8n\pi[/tex]
All real numbers except [tex]x \neq 4\pi + 8n\pi[/tex], where n is any integer.
More can be learned about the domain of a function at https://brainly.com/question/27730656
#SPJ2
