Final answer:
To find (f-g)(x) for the given functions f(x) = -x² + 3x + 5 and g(x) = x² - 2, subtract g(x) from f(x), which results in combining like terms to get (f-g)(x) = -2x² + 3x + 7.
Step-by-step explanation:
To find the function (f-g)(x) when given f(x) = -x² + 3x + 5 and g(x) = x² - 2, you perform subtraction of the functions:
(f-g)(x) = f(x) - g(x)
(f-g)(x) = (-x² + 3x + 5) - (x² - 2)
When you subtract, change the signs of the second function and then combine like terms. Therefore:
(f-g)(x) = -x² + 3x + 5 - x² + 2
Combine the x² terms:
(f-g)(x) = -x² - x² + 3x + 5 + 2
(f-g)(x) = -2x² + 3x + 7
This is the simplified form of (f-g)(x).