Find the Domain arctan(x)

Problem

arctan(x)

Solution

1. Identify the function as the inverse tangent function, denoted as ƒ(x)=arctan(x) or ƒ(x)=tan(x)(−1)

2. Recall the definition of an inverse function's domain, which is the range of the original function.

3. Determine the range of the tangent function g(y)=tan(y) The tangent function outputs all real numbers as y approaches its vertical asymptotes at ±π/2

4. Conclude that since the range of tan(y) is (−∞,∞) the domain of arctan(x) is all real numbers.

Final Answer

Domain of *arctan(x)=(−∞,∞)

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