Question

Найдите область определения функции y=tg2x.

Answer 1

Функция у=tg2x определена при х≠ π/4 + πk, k∈Z.

Answer 2

Finding the Domain of the Function y = tan(2x)

The domain of the function y = tan(2x) can be determined by considering the restrictions on the input values (x) that would result in a valid output for the tangent function.

The domain of the tangent function is restricted by the values for which the cosine function is not equal to zero. This is because the tangent function is defined as the ratio of the sine function to the cosine function, and division by zero is undefined.

The general formula for the domain of the tangent function is: Domain of tan(x): x ≠ π/2 + πk, where k is an integer

For the function y = tan(2x), the domain can be determined by applying the same restriction to the input values (2x) as follows: Domain of y = tan(2x): 2x ≠ π/2 + πk, where k is an integer

This can be further simplified to find the domain of x: Domain of x for y = tan(2x): x ≠ π/4 + πk, where k is an integer

Therefore, the domain of the function y = tan(2x) is x ≠ π/4 + πk, where k is an integer.