AP EAMCET2006MathematicsFunctions
If f: R R is defined by f(x)=x-[x]- 1 2 for x R , where [x] is the greatest integer not exceeding x , then x R: f(x)= 1 2 is equal to :
Options
- AZ , the set of all integers
- BN , the set of all natural numbers
- C, the empty set
- DR
Correct answer
C. , the empty set
Step-by-step solution
f(x)=x-[x]- 1 2 Also f(x)= 1 2 1 2 =x-[x]- 1 2 x-[x]=1 x =1[ x=[x]+ x ] Which is not possible. x R: f(x)= 1 2 is an empty set.