# Finding domain of this function, don't understand it

• Nov 7th 2008, 09:42 AM
mwok
Finding domain of this function, don't understand it
f(x) = x / sqrt(x+4)

x + 4 = 0
x = -4

OK, so the domain can't include -4 BUT why is it all real numbers greater than -4?

Answer: Domain is all real numbers greater than -4
• Nov 7th 2008, 09:47 AM
james_bond
Because in $\displaystyle \sqrt{x}$ $\displaystyle x$ must be greater than or equal to 0 (at least if you want it to be real..;))
• Nov 7th 2008, 09:47 AM
mwok
Quote:

Originally Posted by james_bond
Because in $\displaystyle \sqrt{x}$ $\displaystyle x$ must be greater or equal to 0.

Can't you have a negative inside a square root?
• Nov 7th 2008, 09:51 AM
james_bond
Only if you're familiar with complex numbers, see here.
• Nov 7th 2008, 09:55 AM
mwok
Ahh, thanks!
• Nov 7th 2008, 10:05 AM
mwok
Hmmm, another question...how come this is different then?

f(x) = x / sqrt( abs(x) - 4 )

Answer: (-infinity, -4) U (4, infinity)
• Nov 7th 2008, 10:47 PM
james_bond
$\displaystyle |a| = \begin{cases} a, & \mbox{if } a \ge 0 \\ -a, & \mbox{if } a < 0. \end{cases}$
Can you solve it now?