Final answer:
To find (f-g)(x), subtract g(x) from f(x) and combine like terms, resulting in the simplified form -2x² + 2x + 2.
Step-by-step explanation:
To find the difference of the functions f(x) = -2x² + 3x - 2 and g(x) = x - 4, denoted as (f-g)(x), you simply subtract the function g(x) from f(x). This process is straightforward and involves combining like terms after subtraction.
The difference (f-g)(x) is computed as follows:
f(x) - g(x) = (-2x² + 3x - 2) - (x - 4)
Now distribute the negative sign through the second parenthesis:
= -2x² + 3x - 2 - x + 4
Combine like terms:
= -2x² + (3x - x) - (2 - 4)
= -2x² + 2x + 2
This is the simplified form of (f-g)(x).