Question

9.

((x - 2)2
The function f(x) = ax2 + bx
3x – 6
if x < -1
if - 1 if x 2
is continuous for all real values of x.
Find a and b.

Answer 1

a = 0.3 and b = - 1.1

Explanation:

(x - 2)² = x² -4x + 4

Hence, x² - 4x + 4 = 3x - 6

x² - 7x + 10 = 0

(x - 5)(x - 2) = 0

∴ x = 5 or 2

f(5) = 25a + 5b = 2 ----- (i)

f(2) = 4a + 2b = -1 ------ (ii)

(i) X 2: 50a + 10b = 4 ----- (iii)

(ii) X 5: 20a + 10a = -5 ---- (iv)

Subtract (iv) from (iii): 30a = 9

a = 0.3

Substitute a into (ii) to obtain b

4(0.3) + 2b = -1

2b = -1 - 1.2 = -2.2

∴ b = -1.1