AP EAMCET201726 Apr 2017Morning ShiftMathematicsFunctionsActual
Let N be the set of all natural numbers, Z be the set of all integers and : N Z be defined by (n)= array ccc n 2 , & if & n is even - n-1 2 , & if & n is odd array . . Then,
Options
- Ais onto but not one-one
- Bis one-one but not onto
- Cis neither one-one nor onto
- Dis one-one and onto
Correct answer
D. is one-one and onto
Step-by-step solution
Given that, (n)= array cl n 2 & if n is even - (n-1) 2 & if n is odd array . Case-I : If n is even (n)=1,2,3,4,5, Case-II: If n is odd (n)=0,-1,-2,-3,-4, Thus, for every value of n (n) has an unique image. (n) is one-one function. So, range of (n)=Z Range of (n)= codomain of (n)=Z . Hence, (n) is one-one and onto function.