Question

Find a simplified expression for (F(x)) if (F(x) = left(fgright)(x)), where (f(x) = 12x² - 2x - 2) and (g(x) = 3x + 1).

a) (F(x) = 4x - 23)
b) (F(x) = 4x + 23)
c) (F(x) = 4x - 2x + 3)
d) (F(x) = 4x + 2x + 3)

Answer 1

The simplified expression for F(x) is 108x² + 66x + 8.

Step-by-step explanation:

To find the simplified expression for F(x), we need to substitute the given expressions for f(x) and g(x) into F(x).

Given that f(x) = 12x² - 2x - 2 and g(x) = 3x + 1, substituting these values into F(x), we get:

F(x) = f(g(x)) = f(3x + 1) = 12(3x + 1)² - 2(3x + 1) - 2

Simplifying further:

F(x) = 12(9x² + 6x + 1) - 6x - 2 - 2

F(x) = 108x² + 72x + 12 - 6x - 4

F(x) = 108x² + 66x + 8

Therefore, the simplified expression for F(x) is 108x² + 66x + 8.