Question

If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?

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О-2
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Answer 1

x = -2.

Explanation:

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

= x^2 - 2x + (6x + 4)

= x^2 + 4x + 4.

To find x when this = 0:

x^2 + 4x + 4 = 0

(x + 2)^2 = 0

x = -2.

Answer 2

x = - 2

Explanation:

note that (f + g)(x) = f(x) + g(x)

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

Equating to zero gives

(x + 2)² = 0, that is

x + 2 = 0 ⇒ x = - 2