Y is onto,
you usually suppose that y is any element of Y and show that there
is an element x of X with f(x) = y.5. Recall that a function f is onto if, and only if, for every element y
in the co-domain, there exists an element x in the domain such that f(x) = y. To show that
a function f: XY is onto,
you usually suppose that y is any element of Y and show that there
is an element x of X with f(x) = y.
Let F: RR be defined as F(x) = 2x + 4
for all x in R and we are required to prove that F is onto.
Suppose that y is any real number. Then there exists a real number x such that F(x) = y, namely x = ( y - 4 )/2.
That is, F(x) = F( ( y - 4 )/2 ) = 2 ( y - 4 )/2 + 4 = y.