Final answer:
The expression for (g-f)(x) where f(x) = x² + 2x and g(x) = 2x - 3, is (g-f)(x) = -x² - 3
Step-by-step explanation:
To find the expression for (g-f)(x), first, we are given the functions f(x) = x² + 2x and g(x) = 2x - 3. The operation (g-f)(x) means that we should subtract the function f(x) from the function g(x). Performing the subtraction, we get:
g(x) - f(x) = (2x - 3) - (x² + 2x)
Now, distribute the negative sign to the terms in f(x): g(x) - f(x) = 2x - 3 - x² - 2x
Combine like terms: (g-f)(x) = -x² + 2x - 2x - 3
(g-f)(x) = -x² - 3
The expression for (g-f)(x) is -x² - 3.