Let a, b ∈ R, (a ≠ 0). If the function f defined as f(x) = { 2x²a, 0 ≤ x < 1/a ; a, 1/a ≤ x < √2 ; 2b²√bx³, √2 ≤ x < ∞ } is continuous in the interval [0, ∞), then an ordered pair (a, b) is:

Continuity at x = 1/a:
2(1/a)²a = a
2/a = a
a² = 2
a = ±√2

Continuity at x = √2:
a = 2b²√b(√2)³
a = 2b²√b(2√2)
a = 4√2b²√b

Case 1) Put a = -√2, we get b as complex number.
Case 2) Put a = √2
√2 = 4√2b²√b
1 = 4b²√b
1 = 4b^(5/2)
1/4 = b^(5/2)
(1/4)^(2/5) = b
b = (1/2)^(4/5)