The correct option is D g(x)f(x)
The functions f(x) = 2x and g(x) =x22+1 are polynomial functions and hence, are continuous everywhere.
Therefore,f(x)+g(x), f(x)−g(x), f(x).g(x) are continuous everywhere.
g(x)f(x) is discontinuous where f(x)=0, i.e. x = 0.
f(x)g(x) is discontinuous where g(x) = 0, i.e. x22+1=0⇒x2=−2
No such value of x exists. So, f(x)g(x) is continuous everywhere.