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 Also, given any real
number y in R, there exists 2
y  in R such that f ( 2
y ) = 2 ( 2
y ) = y