Given f(x) = x² + 2 and g(x) = x + 14
Find the values of a such that f(a) = g(a)

a = - 3, a = 4

Step-by-step explanation:

Given f(x) = x² + 2 and g(x) = x + 14 , then

f(a) = a² + 2 and g(a) = a + 14

For f(a) = g(a) , then equate the right sides

a² + 2 = a + 14 ( subtract a + 14 from both sides )

a² - a - 12 = 0 ← in standard form

(a - 4)(a + 3) = 0 ← in factored form

Equate each factor to zero and solve for a

a + 3 = 0 ⇒ a = - 3

a - 4 = 0 ⇒ a = 4