Is this function $f$ onto for all positive integers?
$f(x) = x+2$
$\Bbb Z^+ \to\Bbb Z^+$
what about $1$?
Is this function $f$ onto for all positive integers?
$f(x) = x+2$
$\Bbb Z^+ \to\Bbb Z^+$
what about $1$?
Suppose there is a $x\in\mathbb{Z^+}$ such that $f(x)=1$, then this implies $x+2=1,$ i.e. $x=-1\not\in\mathbb{Z^+}$; so this is a contradiction. Hence $1$ has no preimage in $\mathbb{Z^+}$, which says that the function is not onto.