Consider the following.
f(x)= {-5x, x≤6
{x^2-2x+7, x6
Find the x value at which f is not continuous.
x=?
After using limits for x approaching 6 from the left and right they do not match. The first is -30 and the 2nd is 31. I don't know how else to find the x-value. So I figured it does not exist but this doesn't seem to be correct.

Question

Consider the following.
f(x)= {-5x, x≤6
         {x^2-2x+7, x>6
Find the x value at which f is not continuous. 
x=?
After using limits for x approaching 6 from the left and right they do not match. The first is -30 and the 2nd is 31. I don't know how else to find the x-value.  So I figured it does not exist but this doesn't seem to be correct.

anonymous · Answer

that is it. plug in 6 and see what you get. if the answers are different, then the limit from the left is different from the limit from the right so no limit

anonymous · Answer

for all other values of x these are polynomials, so always continuous