Question

F(x) = x + 2

g(x) = 3x² - 5
Find (f.g)(x).
OA. (f g)(x) = 3x³ - 10
OB. (f g)(x) = 3x³ + 6x² - 5x - 10
OC. (f. g)(x) = 3x³ + 10
OD. (f g)(x) = 3x³ + 6x² + 5x + 10
SUBMIT

Answer 1

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!