AP EAMCET Engineering 2018 Apr 23 Shift 2 Paper

Consider the function,
f(x)={

[x],	if‌x<2
[x]−1	if‌x≥2

At x=2,f(2)=1
So, LHL is,

lim

h→0

[2−h]=1
And RHL is,

lim

h→0

([2−h]−1)=2−1
=1
So, f x( ) is continuous at x = 2 and [x] is continuous in [n,n+1),∀n∈ integer
So, given function is continuous in the interval [1, 3).