f(x) = {x^2-x / (x+1) if x does not = -1
{ 0 if x = -1

Is this graph continuous at x = -1? Please explain! Thanks

Question

f(x) = {x^2-x / (x+1)      if x does not = -1
          { 0                           if x = -1

Is  this graph continuous at x = -1? Please explain! Thanks

lgbasallote · Answer

if x = -1 then what is f(-1)?

helder_edwin · Answer

remember the definition: f is continous at x=-1 if
$$ \large \lim_{x\to-1}f(x)=f(-1) $$

anonymous · Answer

this is not as hard as it looks
replace $x$ by -1 in the expression $\frac{x^2-x}{x+1}$
you will get $\frac{2}{0}$ which is undefined
so forget about it being continuous at -1\
if you got $\frac{0}{0}$ you would have more work to do, but in this case there is nothing to compute after that