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 Show that f and g are one-one, but f + g is not
one-one Solution Since for any two distinct elements x1 and x2 in 0, 2
π






, sin x1 ≠ sin x2 and
cos x1 ≠ cos x2, both f and g must be one-one