Find the Domain 1/2*sin(2x-pi/3)+1

Problem

1/2*sin(2*x−π/3)+1

Solution

1. Identify the type of function provided. The expression is a transformation of the sine function, which is a trigonometric function.

2. Determine the constraints for the input variable x The sine function, sin(θ) is defined for all real numbers θ

3. Analyze the argument of the sine function. In this case, the argument is 2*x−π/3 Since any real value of x will result in a real value for the argument, there are no restrictions on x

4. Conclude that there are no denominators containing x that could be zero, and no square roots of negative numbers, so the domain is all real numbers.

Final Answer

Domain: *(−∞,∞)

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