Final Answer:
The value of (f-g)(x) is 2x³-3x² - 10x + 2.
Step-by-step explanation:
To find the difference of two functions, we can subtract the corresponding terms of each function. In this case, we have:
f(x) = 5x - 2
g(x) = 2x³ - 3x² + 5x - 4
To find (f-g)(x), we can subtract the corresponding terms of each function:
(f-g)(x) = f(x) - g(x)
(f-g)(x) = (5x - 2) - (2x³ - 3x² + 5x - 4)
Distributing the negative sign, we get:
(f-g)(x) = 5x - 2 - 2x³ + 3x² - 5x + 4
Combining like terms, we get:
(f-g)(x) = 2x³ - 3x² - 10x + 2
Therefore, (f-g)(x) = 2x³-3x² - 10x + 2.