Question

If r(x) = 3x² and g(x) = x² - 1, which expression is equivalent to (f g)(x)?

1) (3x²)(x² - 1)
2) (3x²)² - 1
3) (3x²)(x²) - 1
4) (3x²)² + 1

Answer 1

To find (f g)(x), substitute g(x) into f(x) and simplify the expression.

Step-by-step explanation:

In order to find (f g)(x), we need to substitute the expression for g(x) into the function f(x). The function f(x) is given as r(x) = 3x². So, substituting g(x) = x² - 1 into f(x), we get:

(f g)(x) = r(g(x)) = 3(x² - 1)²

Simplifying further, we have:

(f g)(x) = 3(x² - 1)² = 3(x² - 2x + 1) = 3x² - 6x + 3