Further,
f is not onto, as for 1 ∈ N, there does not exist any x in N such that f(x) = 2x = 1 Fig 1 2 (i) to (iv)
Rationalised 2023-24
RELATIONS AND FUNCTIONS
9
Example 9  Prove that the function f : R → R, given by f (x) = 2x, is one-one and onto Solution  f is one-one, as f (x1) = f (x2) ⇒ 2x1 = 2x2 ⇒ x1 = x2