Respuesta :
Answer:
([tex]\frac{1}{3}[/tex], [tex]\frac{16}{3}[/tex] ) and (1, 8 )
Step-by-step explanation:
To find the points of intersection equate f(x) and g(x), that is
3x² + 5 = 4x + 4 ( subtract 4x + 4 from both sides )
3x² - 4x + 1 = 0 ← in standard form
(3x - 1)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
3x - 1 = 0 ⇒ 3x = 1 ⇒ x = [tex]\frac{1}{3}[/tex]
x - 1 = 0 ⇒ x = 1
Substitute these values into either of the 2 functions for corresponding y- coordinates.
Substituting into g(x), then
g(1) = 4(1) + 4 = 4 + 4 = 8 ⇒ (1, 8 )
g([tex]\frac{1}{3}[/tex] ) = [tex]\frac{4}{3}[/tex] + 4 = [tex]\frac{16}{3}[/tex] ⇒ ([tex]\frac{1}{3}[/tex], [tex]\frac{16}{3}[/tex] )
