Question

the range of f(n)=√2{n}-{n}^2-3/4 where {•} is a fractional part of function​

Answer 1

f(x)=[x]2+x−[x]

at x=1

x→1−limf(x)=x→1−lim(02+x+0)

as (x→1−;0<x<1;[x]=0)

=1=1

x→1+limf(x)=x→1+lim(12+x−1)

=1+0=1

as x→1+⇒1<x<2

[x]=1

LHL = RHL =f(1)

at x=n,nϵI−{1}

x→n−limf(x)=(n−1)2+n−(n−1)

=

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