f(x) = [x] 1) f: [0.1) for all Reals is continuous 2) f: (-1,1) for all Reals is
ID: 1944179 • Letter: F
Question
f(x) = [x]
1) f: [0.1) for all Reals is continuous
2) f: (-1,1) for all Reals is not cont at 0
3) f: [0,1] for all Reals is not cont on [0,1]
4) f: [0,1) for all reals is cont on [0,1)
can you explain each of the above.. I would think the entire function would be continuous... why is it not at certain intervals? please explain each... THANKS
Explanation / Answer
f(x)=[x], so f(x)= 0 x->[0,1) =1 x->[1,2) =-1 x->[-1,0) 1> in [0,1)..there is no discontiunuity 2> but in (-1,1)...as we reach 0 from left side left limit...f(0-)=-1.f(0)=0, f(0+)=0...hence right hand and left hand limit donot match 3>in[0,1], again at 1 f[1-]=0, f[1]=1,right hand limit and value of function donot match. so not continuous 4>on [0,1)...f(x)=0....so continuous in the entire range
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