Question

Дана функция у=5sinx+2. Найдите ее область определения, множество заначений и все значения х, при которых у=–3

Answer 1

Сорь за качество, но см приложение

Answer 2

Function Analysis

The given function is y = 5sin(x) + 2. Let's analyze this function step by step.

Domain of the Function

The domain of the function is the set of all possible input values (x) for the function. For the function y = 5sin(x) + 2, the domain is all real numbers, as there are no restrictions on the values of x.

Range of the Function

The range of the function is the set of all possible output values (y) for the function. For the function y = 5sin(x) + 2, the range is [2, 7]. This is because the sine function's range is between -1 and 1, and when multiplied by 5 and added to 2, it shifts the range to [2, 7].

Values of x when y = -3

To find the values of x when y = -3, we can solve the equation 5sin(x) + 2 = -3 for x.

5sin(x) + 2 = -3 5sin(x) = -5 sin(x) = -1 x = arcsin(-1)

The solutions for arcsin(-1) are x = -π/2 + 2πn, where n is an integer.

Therefore, the values of x when y = -3 are x = -π/2 + 2πn, where n is an integer.

Conclusion

In summary, the domain of the function y = 5sin(x) + 2 is all real numbers, the range is [2, 7], and the values of x when y = -3 are x = -π/2 + 2πn, where n is an integer.