Answer:
(- 2, 11 ) and (- 1, 6 )
Explanation:
Equate the right side of both, that is
x² - 2x + 3 = - 5x + 1 ( subtract - 5x + 1 from both sides )
x² + 3x + 2 = 0 ← in standard form
(x + 2)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x + 1 = 0 ⇒ x = - 1
Substitute these values into f(x) = - 5x + 1
f(- 2) = - 5(- 2) + 1 = 10 + 1 = 11 ⇒ (- 2, 11 )
f(- 1)= - 5(- 1) + 1 = 5 + 1 = 6 ⇒ (- 1, 6 )