Show that although IN is onto but IN + IN : N → N defined as
(IN + IN) (x) = IN (x) + IN (x) = x + x = 2x is not onto Rationalised 2023-24
RELATIONS AND FUNCTIONS
15
Solution Clearly IN is onto But IN + IN is not onto, as we can find an element 3
in the co-domain N such that there does not exist any x in the domain N with
(IN + IN) (x) = 2x = 3 Example 26 Consider a function f : 0, 2
π

→




R given by f (x) = sin x and
g : 0, 2
π

→




R given by g(x) = cos x