Draw the graph of `y= [x]+ sqrt(x-[x])`, where`[*]` denotes the greatest ineger function.

Explanation

`y= f(X) = [x] + sqrt(x-[x])`
For `0 le x lt 1, y = sqrtx`, the graph of which is part of parabola `y^(2)=x` lying above the x-axis.
For `1 le x lt 2, y=1 + sqrt(x-1)`, the graph of which is part of the parabola `(y-1)^(2)=x-1` lying above the axis of the parabola `y=1`.
Thus, all the branches of `y=f (x) ` are part of different parabolas.
Also we can see that in each interval `y= f(x)` is an increasing function.
Hence the graph of`y= f(x)` is as shown in the following figure.