Thread: Domain of a function?

I have a multiple choice question in my workbook, Im not sure what the answer might be. If anyone could tell me and explain why, that would be great.

The domain of the function y = tan x is:

a) x ∈ R
b) -1<x<1
c) x ≠ nπ, where N ∈1
d) x ≠(π/2) + nπ, where N ∈1

Please note: π = Pi!

Thank you!

Originally Posted by DUB_008

I have a multiple choice question in my workbook, Im not sure what the answer might be. If anyone could tell me and explain why, that would be great.

The domain of the function y = tan x is:

a) x ∈ R
b) -1<x<1
c) x ≠ nπ, where N ∈1
d) x ≠(π/2) + nπ, where N ∈1

Please note: π = Pi!

Thank you!

The tangent function can take on any real number except values that make cosine zero because you cannot divide by zero. Note that tangent is sine divided by cosine, so if cosine is zero, then tangent is undefined. The domain can be thought of as the input or as the x variable in the 2-D grid.

The multiple choices are meant to throw you off. Answer A would be a popular wrong choice that was picked because a person may have forgotten to think about cases where the function is undefined. Answer B is the range (output, y/f(x) values) excluding -1 and 1 of course. Answer C are all reals excluding the values where sine is zero and consequently tangent is zero. Answer D are all reals excluding the values where cosine is zero and consequently tangent is undefined. Tangent is defined for that region, so that is your answer.