Answer:
To find the domain of (f + g)(x), we need to consider the domains of both f(x) and g(x) and determine any restrictions or limitations.
1. For f(x) = -x + 2, there are no restrictions on the domain. We can input any real number for x, and the function will give us a valid output.
2. For g(x) = √(-x), the square root function has a restriction. The value inside the square root, -x, must be greater than or equal to 0 to have a real square root. Therefore, we need -x ≥ 0.
Solving -x ≥ 0, we multiply both sides by -1, which reverses the inequality: x ≤ 0.
Combining the domain restrictions for f(x) and g(x), we have:
- For f(x), the domain is all real numbers.
- For g(x), the domain is x ≤ 0.
To find the domain of (f + g)(x), we need to consider where both f(x) and g(x) are defined. In this case, both functions are defined for all x.
Therefore, the domain of (f + g)(x) is all real numbers.