draw the graphs of:
(1) [x] + √{x}
(2) [|x|] + √{|x|}
(3) |[x]| + √|{x}|
(4) |[x]| + √{x}
{ }-------->fractional part ; | | ------------>modulus ; [ ] ------------>greatest integer function
be careful with the signs...this question is bit out of sorts but still tallies with jee standards............i expect help from ones like nishant sir and kaymant sir !!!!
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2 Answers
1(1) for any integer n, n <= x < n+1
y = [x] + √{x} = n + √(x-n)
so the curve will be a set of part of parabolas (y-n)2=(x-n)
it will be continuous but non-differentiable at integral points (a pointed curve at integral points)
(2) If we replace x by -x there is no change in the function, so the curve is symmetrical about y-axis
so draw the graph as in (1) in 1st quadrant and plot its reflection in 2nd quadrant.
(3) and (4) are same as fractional part is non-negative. Try it
