f : N → N : f(x) = x^2 + x + 1 is A. one - one and onto B. one - one and into C. many - one and onto D. many - one and into

Question

Mark (√) against the correct answer in the following: 

f : N → N : f(x) = x² + x + 1 is 

A. one - one and onto 

B. one - one and into 

C. many - one and onto 

D. many - one and into

Answer 1

Correct Answer is (B) . one - one and into

In the given range of N f(x) is monotonically increasing.

∴f(x) = x² + x + 1 is one one.

But Range of f(n) = [0.75,∞)≠N(codomain)

Hence, f(x) is not onto.

Hence, the function f : N → N : f(x) = (x² + x + 1) is one - one but not onto. i.e. into