Find the Domain sin(pix)

Problem

sin(π*x)

Solution

1. Identify the function type. The given expression is a sine function, where the argument is a linear expression π*x

2. Recall the properties of the sine function. The function sin(θ) is defined for all real numbers θ

3. Analyze the argument. Since the argument π*x is a polynomial (specifically a linear function), it is defined for all real values of x

4. Determine the domain. There are no square roots of negative numbers, logarithms of non-positive numbers, or denominators that could be zero. Therefore, x can be any real number.

Final Answer

Domain: *(−∞,∞)

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