How can I find the range and codomain for the function F

Question

Let A={a,b,c},B={x,y,z},C={r,s,t} ... Let f:A→B and g:B→C be defined by: f={(a,y)(b,x),(c,y)} and g={(x,s),(y,t),(z,r)}

How can I find the range of f and the codomain of f. ??

Answer 1

The notation $f:A \rightarrow B$ indicates that $f$ is mapping elements fom the set $A$ to elements from the set $B$. That immediately tells you that the codomain is $B$. No need to look at which specific elements get mapped to which specific elements. It is, as the commenter expresses it, the a priori or intended destination. Think of it as the 'y-axis' when graphing some function $y=f(x)$

The range is the set of elements from the codomain that the function actually maps to. So now you do need to look at which elements map to which elements. So, looking at that, we see that the function maps to the elements $x$ and $y$ only (nothing gets mapped to $z$). Therefore, the range is $\{ x,y\}$