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 b are -

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

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

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

D) None of these