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find the range of y=[x]+[-x] where[] denotes G.I.F.

find the range of y=[x]+[-x]  where[] denotes G.I.F.

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Manmohan,

 

To find out the range, you need to find the entire interval in which 'y' lies for all values of 'x' in the domain.

 

Here clearly domain is the entire set of real numbersd.

 

Here we will consider two cases..... (1) x is an integer, and (2) x is a non-integer.

 

(1) when x is an integer [x] = x and [-x] = -x, so sum is 0..... ie y = 0 when x is integer.

(2) when x is non-integer: consider that x is positive, in that case [-x] = -[x] - 1.... so sum = -1..... ie y = -1 when x is a positive non integer.

similarly, when x is a negative non-integer.... [x] = -[-x]-1..... so again y = -1.

 

So 'y' can take only two values : 0, -1..... Hence the range is the set of two numbers viz. {-1,0}.

 

Hope that helps!!!!

Regards,

Ashwin (IIT Madras)

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