154787

The upper bound is the value of x when x^0.5+1/x^0.5= 4.
Firstly everything is multiplied by x^0.5 then 4 is squared giving us x+1=4(x^0.5)=16x^0.5
Then everything is squared giving us x^2+2x+1= 16x
16x are subtracted giving us x^2 +14x+1=0
Using the quadratic formula: x= 7+-48^0.5
We need the highest value so the upper band is 7+48^0.5

Lower bound is 0 since any value larger than 0 is positive and anything smaller than the upper band that is positive will give an answer less than 4.

The range of values of x is 0<x<7+48^0.5.