Question

If f(x) = 3x^2 -2x-1 and g(x) = x^2 find (gof) (x)

Answer 1

A

Explanation:

Substitute x = f(x) into g(x), that is

g(f(x))

= g(3x² - 2x - 1)

= (3x² - 2x - 1)² = (3x² - 2x - 1)(3x² - 2x - 1)

Each term in the second factor is multiplied by each term in the first factor, that is

3x²(3x² - 2x - 1) - 2x(3x² - 2x - 1) - 1(3x² - 2x - 1) ← distribute parenthesis

= 9
`x^(4)` - 6x³ - 3x² - 6x³ + 4x² + 2x - 3x² + 2x + 1 ← collect like terms

= 9
`x^(4)` - 12x³ - 2x² + 4x + 1 → A