Question

Y=1+2sinx область определения и область значения найдите, пожалуйста

Answer 1

область определения от минус бесконечности до плюс бесконечности, область значения [1,5;2,5]

Answer 2

Equation and Domain

The equation is y = 1 + 2sin(x). Let's determine the domain and range of this equation.

The domain of the equation refers to the set of all possible input values for the variable x. In this case, since the sine function is defined for all real numbers, there are no restrictions on the domain. Therefore, the domain of the equation is all real numbers.

Range

To find the range, we need to determine the set of all possible output values for the variable y. The range of the equation can be determined by analyzing the behavior of the sine function.

The sine function oscillates between -1 and 1, inclusive. Multiplying the sine function by 2 and adding 1 shifts the range upward by 1 unit. Therefore, the range of the equation is [1, 3].

To summarize: - Domain: all real numbers - Range: [1, 3]

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