The range of the function y = inverse tan(2x) is definitively (-π/2, π/2). The transformation of the input variable x by the factor of 2 affects the domain but does not alter the established range of the inverse tangent function. As x approaches negative infinity, 2x also approaches negative infinity, leading tan-1(2x) to approach -π/2. Conversely, as x approaches positive infinity, 2x approaches positive infinity, resulting in tan-1(2x) approaching π/2.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone seeking to understand the properties of inverse trigonometric functions.