Explain why the function is discontinuous at the given number a.

f(x)=ln l x-2 l a=2

I don't understand how I would explain this.. in the back of the book it said f(2) is not defined. What do they mean by that?

1 answer

Your f(x) has an "=" sign in it, before the 2. That must be a misprint. You do not define a function using 2 equals signs.

The log of zero, to any base, is not defined. It is -infinity.

If e^a = 0, then a would be ln 0. No matter how many times you multiply e by itself, you cannot get zero. If a is a large negative number, e^a approaches zero but never gets there. Thefore ln 0 doies not exist (or is "undefined")