What is the domain of arctan(x)?

Chana Rivera

Chana Rivera

Answered question

2023-02-02

What is the domain of arctan ( x ) ?

Answer & Explanation

Marcel Yoder

Marcel Yoder

Beginner2023-02-03Added 4 answers

The function tan ( x ) is a many to one periodic function, so to define an inverse function requires that we restrict its domain.
To define arctan ( x ) as a function we can restrict the domain of tan ( x ) to ( - π 2 , π 2 ) . The function tan ( x ) is one to one, continuous and unbounded over this interval, so has a well defined inverse arctan ( x ) : ( - π 2 , π 2 ) that is also continuous and one to one.

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