Question

If r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to (f g) (x)?

1) (r s) (x)
2) (s r) (x)
3) (r + s) (x)
4) (r - s) (x)

Answer 1

The expression (f g)(x) is equivalent to 6x + 2.

Step-by-step explanation:

The expression (f g)(x) represents the composition of functions f(x) and g(x), which is written as f(g(x)). To find the equivalent expression, we substitute the function g(x) into function f(x).

Given f(x) = 3x – 1 and g(x) = 2x + 1, to find (f g)(x), we substitute g(x) into f(x):

(f g)(x) = f(g(x)) = f(2x + 1) = 3(2x + 1) - 1 = 6x + 3 - 1 = 6x + 2.

Therefore, the expression that is equivalent to (f g)(x) is 6x + 2. The correct option is 6x + 2.