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<∞} is continuous in the interval…

Let $\displaystyle a, b \in \mathbf{R},(a \neq 0)$. If the function $\displaystyle f$ defined as $$f(x)= \begin{cases}\frac{2 x^2}{a}, & 0 \leq x<1 \\ a, & 1 \leq x<\sqrt{2} \\ \frac{2 b^2-4 b}{x^3}, & \sqrt{2} \leq x<\infty\end{cases} $$ is continuous in the interval $\displaystyle [0, \infty)$, then an ordered pair $\displaystyle (a, b)$ is :