At which value(s) is the expression 1/x undefined?

When a function/expression is "undefined", their denominator would equal to zero. 

When would f(x)=1/0? When x=0! 

Therefore, when x=0, the function would become undefined. 

If you have a more complex function such as 1/2x+3 and you want to find the point it becomes undefined, 

Make 2x+3=0 and find x. 

2x+3=0 
2x=-3 
x=-3/2 (at this point it becomes undefined) 

Hope I helped :)