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the range of the function f(x)=x-[x]/1+x-[x].where[.] is gretest integer function.
hi preet
y = { x } / 1 + { x }
domain is ] - infinity , + infinity [
we know 0 < { x } < 1
so 0 < { x } / 1 + { x } < 1
{x}/1+{x}
= 1 – 1/1+{x}
Since 0<={x}<1;
1<= 1+{x} <2
ð ½<1/1+{x}<=1
ð -1<= -1/1+{x} < -0.5
ð 0<= 1- 1/1+{x} <0.5
There fore the given sum ranges from [0,0.5)
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