Let a , b ∈ R , a ≠ 0 . If the function f , defined as f x = 2 x 2 a , 0 ≤ x < 1 a , 1 ≤ x < 2 2 b 2 - 4 b x 3 , 2 ≤ x < 8 ,is continuous in the interval 0 , ∞ , then an ordered pair a , b can be

Step-by-step solution

Here, f x is continuous at x = 1  ⇒ lim x → 1 - f x = lim x → 1 + f x ⇒ 2 a = a     ⇒ a =   ±     2 Since, f ( x ) is continuous at x = 2 ⇒ lim x → 2 - f x = lim x → 2 + f x ⇒ a = 2 b 2 - 4 b 2 2 Put a =   2 ⇒ 2 = b 2 - 2 b     ⇒ b 2 - 2 b - 2 = 0 ⇒ b = 2±   4 + 4.2 2 = 1 ±   3 Hence, a , b ≡ 2 , 1 ± 3