Question $2\mathrm{.}3\mathrm{.}0\mathrm{.}25\mathrm{.}141.$ Given the function

$f(x)=\{\begin{array}{ccc}\frac{x^2-4}{x-2}& if& x<mn>2</mn>\\ a{x}^2-bx+3& if& 2x<mn>3</mn>\\ 2x-a+b& if& x3\end{array}$

For which values of $a,b$ the function is continuous on $R.$

A$.a=\frac{1}{2},b=0.$

B$.a=0,b=2.$

C$.a=\frac{1}{2},b=\frac{1}{2}.$

D$.a=\frac{1}{2},b=3.$