Question

Hello, I really need help solving this. It is a practice problem from my ACT prep guide. The subject is trigonometry. The answer options are at the bottom, *one answer per box*

Answer 1

To find the domain of the function f(x)=tanx restricted so that its inverse function exists

we know that,

Since the range of tan inverse x is (-π/2, π/2), the answer should lie in this interval. Assume that y = tan -1 x. Then by the definition of inverse tan, tan y = x. The value of y in the interval (-π/2, π/2) that satisfies the equation tan y = x .

The domain of tanx is restricted to (-π/2, π/2). The range of tanx is always real numbers.

we get that,

The domain of f(x)=tanx is restricted to (-π/2, π/2) so that the inverse function exists. This means that all functional values of f(x)=tan^-1 x are on the interval (-π/2, π/2).