Question

Composite Functionsf(x) = 2x³ g(x) = x - 3 Find f(2) Find (f + g)(x)

A) 2x^3 + x - 3
B) 2x^3 - x + 3
C) 2x^3 - 3x
D) 2x^3 + x

Answer 1

To find f(2), substitute 2 into the function f(x) = 2x³. To find (f + g)(x), add the two functions: f(x) + g(x). Therefore, the answer is (f + g)(x) = 2x³ + x - 3, which corresponds to option B.

Step-by-step explanation:

To find f(2), we substitute 2 into the function f(x) = 2x³:

f(2) = 2(2)³ = 2(8) = 16

To find (f + g)(x), we add the two functions:

(f + g)(x) = f(x) + g(x) = 2x³ + (x - 3)

Therefore, the answer is (f + g)(x) = 2x³ + x - 3, which corresponds to option B.