Final answer:
To find (f-g)(x), subtract the function G(x) from the function f(x) and combine like terms.
Step-by-step explanation:
To find (f-g)(x), we need to subtract the function G(x) from the function f(x). The function f(x) is given as f(x) = 2x² - 5 and G(x) is given as G(x) = 3x + 3.
Replacing f(x) with its given expression and G(x) with its given expression, we have (f-g)(x) = (2x² - 5) - (3x + 3).
Simplifying the expression by distributing the negative sign, we get (f-g)(x) = 2x² - 5 - 3x - 3.
Combining like terms, we have (f-g)(x) = 2x² - 3x - 8.