For f(x)= Ln(x) at point xe and (x/e) at x

Question

For f(x)= Ln(x) at point x>e and (x/e) at x<or equal to e, is f(x)...?
A.) f(x) is differentiable but not continuous at x = e 
B.) f(x) is neither continuous nor differentiable 
C.) f(x) is undefined at x = e 
D.) f(x) is continuous but not differentiable at x = e
E.) f(x) is continuous and differentiable everywhere

anonymous · Answer

ok... to see if function is continuous or not, just take the limit. First, is the function defined at  x=e?

anonymous · Answer

in other words, do you get a real number when you evaluate f(e)

anonymous · Answer

Then plug e into ln(x), to see if f(e) = ln(e). If they are equal, then you have a continuous function

anonymous · Answer

continuity also implies differentiability, so if your function is continuous, then it's also diff'able

anonymous · Answer

ln(e)=1 and f(e)=1
I think the answer would be E.

anonymous · Answer

yup, seems right

anonymous · Answer

Thank you.