Question

Determine where f is continuous when f(x)=(lnx)^2?

Answer 1

`0 < x < oo`

Explanation:

.

`f(x)=(lnx)^2`

Since the function has a logarithm in it, `x > 0` because we can not have logarithm of negative numbers.

There is no value of `x` that would make `y` undefined. Therefore, the function is continuous between `x=0 and oo`.

There is a more formal process for testing whether a function is continuous within a certain domain:

A function f(x) is said to be continuous on a closed interval [a, b] if the following conditions are satisfied:
-f(x) is continuous on [a, b];
-f(x) is continuous from the right at a;
-f(x) is continuous from the left at b.

This function passes these tests as well.

The graph of the function is shown below and makes its continuity obvious: