question_answer

The function \[f\,(x)=\left\{ \begin{matrix}    {{x}^{2}}/a & 0\le x<1  \\    a & 1\le x<\sqrt{2}  \\    (2{{b}^{2}}-4b)/{{x}^{2}} & \sqrt{2}\le x<\infty   \\ \end{matrix} \right.\] is continuous for \[0\le x<\infty ,\] then the most suitable values of a and bare

A) \[a=1,\] \[b=-1\]

B) \[a=-1,\] \[b=1+\sqrt{2}\]

C) \[a=-1,\] \[b=1\]

D) none of these