The correct option is C (1, 73]
Let y=f(x)=x2+x+2x2+x+1; xϵR
∴ y=x2+x+2x2+x+1,
y=1+1x2+x+1 [i.e y>1] . . . (i)
⇒yx2+yx+y=x2+x+2⇒x2(y−1)+x(y−1)+(y−2)=0,∵xϵR⇒D≥0⇒(y−1)2−4(y−1)(y−2)≥0⇒(y−1){(y−1)−4(y−2)}≥0⇒(y−1)(−3y+7)≥0
⇒1≤y≤73 . . . (ii)
From (i) and (ii), we get
1<y≤73