I've got a task, where a set A and a map g were given. The task was to calculate g(A). And I don't know what to do exactly, so I'd appreciate if s.o. could explain it with an example or give me a link, where it's explained.
For example let A = { x in IR | |x-3|= 2 } and g (x) = (x+2)/x.
So if I want to calculate g (A) shall I look at ( |x-3|+2)/|x-3| and not look at the whole domain but at {1,5} ?
Thank you
You want to answer the question "what values are mapped to by $g$, from elements in $A$?". So, once you know what $A$ is, in the simplest case you just apply $g$ to the elements of $A$.
As you have already implicitly stated, after simplification we have $A = \{1,5\}$. Therefore, the set we seek is $g(A) = \{g(1),g(5)\}=\left\{3,\frac{7}{5}\right\}$.
Things could have been more complicated, for example if $A$ were not a finite set or if $g$ were a more complicated function: very often in such situations it can be helpful to draw the graph of $g$ (if possible) and mark on the $x$-axis "where $A$ is". In this situation that's not really necessary (but not unhelpful!), since $A$ is finite.