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
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Because in $\displaystyle \sqrt{x}$ $\displaystyle x$ must be greater than or equal to 0 (at least if you want it to be real..)
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?
Only if you're familiar with complex numbers, see here.
Ahh, thanks!
Hmmm, another question...how come this is different then? f(x) = x / sqrt( abs(x) - 4 ) Answer: (-infinity, -4) U (4, infinity)
$\displaystyle |a| = \begin{cases} a, & \mbox{if } a \ge 0 \\ -a, & \mbox{if } a < 0. \end{cases}$ Can you solve it now?
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