Question

What is the domain of the function y=tan(x/8)?

A. all real numbers except 4 pi+4npi, where n is any integer
B. all real numbers except 8pi+4npi, where n is any integer
C. all real numbers except 8pi+8npi, where n is any integer
D. all real numbers except 8pi+8npi, where n is any integer.

Answer 1

The domain of the function y = tan(x/8) is all real numbers except 4π + 4nπ, where n is any integer, which corresponds to option A.

Step-by-step explanation:

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. The function y = tan(x/8) is undefined where the tangent function has asymptotes, which occur at odd multiples of π/2 (90 degrees). For the function y = tan(x/8), this is when x/8 is an odd multiple of π/2, meaning that the asymptotes occur when x = 8(π/2 + nπ), where n is any integer. Therefore, the domain of y = tan(x/8) is all real numbers except x = 4π(2n+1), where n is any integer.

Option A, which states the domain is 'all real numbers except 4π + 4nπ, where n is any integer' correctly identifies the points where the function is undefined due to the periodic nature of the tangent function.