Locate the discontinuities of the function.

Question

Locate the discontinuities of the function.

$$f(x) = \ln(\tan(x)^2)$$

Question is looking for a, $x =$ value.

Answer 1

Hint: Where is $\tan x$ defined? You will not have to worry about it being negative since it has been kindly squared. When is it zero?

Answer 2

Hint: $\tan x = \frac{\sin x}{\cos x}$.

Answer 3

Begin by analyzing the domain of some functions...

What's the domain of $\tan x$?

$x \neq \frac{\pi}{2} + \pi n$ where $n$ is an integer

What's the domain of $\ln x$?

x > 0

What's the domain of $\tan ^2 x$?

same as the domain of $\tan x$

Now look at the ranges of some functions...

What's the range of $\tan x$?

all real numbers (i.e. $(-\infty, \infty)$)

What's the range of $\tan^2 x$?

all non-negative numbers (i.e. $[0, \infty)$)

Now, put it all together.