Prove that the function f: NN, defined by f(x) = x2 + x+1 is one one but not onto. Share with your friends Share 11 Manish Bharti answered this 23 View Full Answer Bhumika Jain answered this f(x) = x2+x+1 Let x1, y1 N such that f(x1) = f(y1) x12+ x1+1 =y12 + y1 + 1=(x1 - y1) (x1+y1+1) = 0 [As x1+y1+1 for any N] x1=y1 f is one-one function Clearly f(x) = x12 + x+1 > 3 for x E N But f(x) does not assume values 1 and 2 f:N N is not onto function f:N N is not onto functionf(x) = x2+x+1 14
