Final answer:
To evaluate (f-g)(4) where f(x)=4x-3 and g(x)=x³+2x, subtract g(x) from f(x), simplify the expression, and then substitute x = 4.
Step-by-step explanation:
To find (f-g)(4), we need to subtract g(x) from f(x) and evaluate the result at x = 4.
Given that f(x) = 4x - 3 and g(x) = x³ + 2x, we have:
(f-g)(x) = f(x) - g(x) = (4x - 3) - (x³ + 2x)
Simplifying the expression, we get (f-g)(x) = 4x - 3 - x³ - 2x
Further simplifying, we have (f-g)(x) = -x³ + 2x - 3
Now, substitute x = 4 into the expression to find (f-g)(4):
(f-g)(4) = -(4)³ + 2(4) - 3
Calculating the values, we get (f-g)(4) = -64 + 8 - 3 = -59.