Question

If f(x) = х2 – 2x and g(x) = 6х +4, for which vаluе оf x does (f + g)(x) = 0?

Answer 1

x = - 2

Explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = x² - 2x + 6x + 4 = x² + 4x + 4

Equating to zero, that is

x² + 4x + 4 = 0 ← left side is a perfect square

(x + 2)² = 0, thus

x + 2 = 0 ⇒ x = - 2

Answer 2

`\boxed{\text{x = -2}}`

Explanation:

ƒ(x) = x² - 2x

g(x) = 6x + 4

(f + g)(x) = x² - 2x + 6x + 4 = x² + 4x + 4

`\begin{array}{rcr}x^(2) + 4x + 4 & = & 0\\(x + 2)^(2) & = & 0\\x+2 & = & 0\\x & = & \mathbf{-2}\\\end{array}`

`(f + g)(x) = 0 \text{ when } \boxed{\textbf{x = -2}}`

Check:

`\begin{array}{rcl}(-2)^(2) + 4(-2) + 4 & = & 0\\4 - 8 + 4 & = & 0\\0 & = & 0\\\end{array}`

OK.