Answer
$f(x) + g(x) = 2x^2 + x + 5$
The domain, meaning the possible $x$ values, is the set of all real numbers.
$f(x) - g(x) = 2x^2 - x + 11$
The domain, meaning the possible $x$ values, is the set of all real numbers.
Work Step by Step
Add the two functions $g(x)$ and $f(x)$:
$f(x) + g(x) = (2x^2 + 8) + (x - 3)$
Use distribute property to get rid of the parentheses, paying attention to the signs:
$f(x) + g(x) = 2x^2 + 8 + x - 3$
Combine like terms:
$f(x) + g(x) = 2x^2 + x + 5$
The domain, meaning the possible $x$ values, is the set of all real numbers.
The second part of the exercise is asking to subtract $g(x)$ from $f(x)$:
$f(x) - g(x) = (2x^2 + 8) - (x - 3)$
Distribute to get rid of the parentheses, paying attention to the signs:
$f(x) - g(x) = 2x^2 + 8 - x + 3$
Combine like terms:
$f(x) - g(x) = 2x^2 - x + 11$
The domain, meaning the possible $x$ values, is the set of all real numbers.
