If f(x)=x2+1[x], ([⋅] denotes the greatest integer function), 1 ≤ x < 4, then

We have, f(x)=x2+1[x]When x ∈ [1, 2) then f (x) = x2 + 1 ⇒ Rf = [2, 5).When x ∈ [2, 3) then f(x)=x2+12⇒Rf=52,5.When x ∈ [3, 4) then f(x)=x2+13⇒Rf=103,173.∴ Rf = [2, 17/3).