Convert the domain of the Tan function to interval notation?

  • Thread starter Tsubaki
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Homework Statement


Hey guys. So basically I'm doing some Calc I homework and I'm working on the domain of this function:

g(x) = √tan(2x+π)

Homework Equations



Now to determine the domain, I know that the function under the root cannot be negative.

The Attempt at a Solution



So after examining the behaviour of tan on different intervals and only allowing positive tan values, I came to the conclusion that the domain of the function should be:

nπ/2 ≤ x ≤nπ/2 + π/4

But the part I'm stuck is converting the domain above into "Interval Notation", as the problem asks. I am used to these domains coming out as nice set intervals, such as (-∞, 2) ∪ (4, +∞), but i'm not seeing that here.

I'd appreciate the assistance. Thanks!

Matt
 

Answers and Replies

  • #2
34,686
6,394

Homework Statement


Hey guys. So basically I'm doing some Calc I homework and I'm working on the domain of this function:

g(x) = √tan(2x+π)

Homework Equations



Now to determine the domain, I know that the function under the root cannot be negative.

The Attempt at a Solution



So after examining the behaviour of tan on different intervals and only allowing positive tan values, I came to the conclusion that the domain of the function should be:

nπ/2 ≤ x ≤nπ/2 + π/4

But the part I'm stuck is converting the domain above into "Interval Notation", as the problem asks. I am used to these domains coming out as nice set intervals, such as (-∞, 2) ∪ (4, +∞), but i'm not seeing that here.

I'd appreciate the assistance. Thanks!

Matt
Maybe something like this:
$$\bigcup_{n \in \mathbb{Z}} [n \pi/2, n\pi/2 + \pi/4)$$
The above represents the union over an index in the integers of the half-open intervals listed.
 

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