Answer
$-2g(x) + f(x) = -2x^2 + 7x - 6$
$\text{The domain is all real numbers.}$
Work Step by Step
In this problem, we are asked to add two functions. Let us go ahead and set up the addition problem, separating the two functions with parentheses:
$-2g(x) + f(x) = -2(x^2 - 3x + 2) + (x - 2)$
Use distributive property to remove the parentheses, but pay attention to the operation in front of the parentheses:
$-2g(x) + f(x) = -2x^2 + 6x - 4 + x - 2$
Group like terms:
$-2g(x) + f(x) = -2x^2 + (6x + x) + (- 4 - 2)$
Combine like terms:
$-2g(x) + f(x) = -2x^2 + 7x - 6$
There are no restrictions on the variable.
The domain is all real numbers since no value of $x$ will make the expression/function undefined.