Where function is continuous?

$$\\f(x)= \frac{\sqrt{x+10}}{x^{3}-16x}\\\\
f(x)= \frac{\sqrt{x+10}}{x(x^{2}-16)}\\\\
f(x)= \frac{\sqrt{x+10}}{x(x-4)(x+4)}\\\\
$You cannot divide by 0 so x cannot be 0,4 or -4$\\\\
$The function is discontinuous at x=0, x=4 and x=-4$\\\\
$In latex, the backslash indicates that a function will follow, $\\
$the arguments of the function usually have to go in parentheses. $\\
$The only exception is some very simple functions where it is assumed$\\
$that just the next entry is the argument. $ ex. \sqrt9$$

His how you do square root in LaTex.

\sqrt

$$\sqrt$$

If you need to know more symbols, like infinity, just ask.

Symbols time!

Infinity:

\infty

$$\infty$$

Fraction:

\frac{}

$$\frac{1}{2}$$

Arrows:

\Leftarrow       \Rightarrow        \Leftrightarrow

$$\Leftarrow$$                   $$\Rightarrow$$                       $$\Leftrightarrow$$

Signs for equality:

\approx

$$\approx$$

Finally, the answer box.

\fbox{\begin{minipage}{0.6cm}\hfill\vspace{0.6cm}\end{minipage}} 

$$\fbox{\begin{minipage}{0.6cm}\hfill\vspace{0.6cm}\end{minipage}}$$ 

Example for answer box:

2+2=\fbox{\begin{minipage}{0.2cm}\44\vspace{0.3cm}\end{minipage}}

$$2+2=\fbox{\begin{minipage}{0.2cm}\44\vspace{0.3cm}\end{minipage}}$$

Ah, okay. So I can just list where the function is discontinuous as the answer for questions like this? I can't find any similar problems in my Calc textbook :/

Also, thanks for the helpful list DragonSlayer :)

Pure welcomness. At your service.

Well, you would show the working the same as I did.

But the question actually asks you for where it is continuous.

So the answer would be

continuous when

x<-4, -4<x<0, 0<x<4, and x>4

OR

$$(-\infty,-4), (-4,0), (0,4), (4,+\infty)$$