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

Problem

sin(2*x−π/3)

Solution

1. Identify the type of function. The given expression is a sine function of the form ƒ(x)=sin(g(x)) where g(x)=2*x−π/3

2. Determine the domain of the inner function. The inner function g(x)=2*x−π/3 is a linear polynomial, which is defined for all real numbers.

3. Determine the domain of the outer function. The sine function sin(u) is defined for all real numbers u in the interval (−∞,∞)

4. Conclude the domain. Since there are no restrictions such as denominators being zero or square roots of negative numbers, the domain is the set of all real numbers.

Final Answer

Domain:(−∞,∞)

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