Perform the indicated operation and state the domain. Let f(x)=x-1 and g(x)=x+1

f(x) - g(x)

Heres my work
(x-1) - (x+1)
x-x=0 and -1-1=-2
Answer =-2 because the x's cancel each other out.
How do i find the domain when there is no x in the answer?

The domain of a constant (-2) is ℝ.

The other way to figure it out is
the domain of f(x) is ℝ
the domain of g(x) is ℝ
From the closure property of subtraction of real numbers, the domain of f(x)-g(x) is also ℝ.

Thanks. What does that symbol mean? and how do i write it?

The symbol means all real numbers, or all numbers between -∞ to +∞ (negative infinity to positive infinity).

It is written as a capital R, with a double stroke on the first.

OK THANKS!

You're welcome!

To find the domain when there is no "x" in the answer, we need to consider the domains of the individual functions being operated on.

In this case, we have two functions: f(x) = x - 1 and g(x) = x + 1. Both of these functions are defined for all real numbers because there are no restrictions or limitations on the domain.

When we perform the operation f(x) - g(x), we are subtracting two functions, which is also defined for all real numbers.

Therefore, the domain of the expression f(x) - g(x) is also all real numbers.