AP EAMCET2012MathematicsFunctions
If f: Z Z is defined f(x)= array lll x 2 , & if & x is even 0, & if & x is odd array . , then f is
Options
- Aonto but not one-to-one
- Bone-to-one but not onto
- Cone-to-one and onto
- Dneither one-to-one nor onto
Correct answer
A. onto but not one-to-one
Step-by-step solution
Given, f: Z Z, f(x)= array l x 2 , if x is even 0, if x is odd array . when x is odd, f(1)=f(3)=0 f(x) is not one-one function. when x is even i.e., x=0, 2, 4, 6, x 2 =0, 1, 2, 3, Hence, range of f is Z . So, it is onto. Hence, f is not one-one but it is onto.