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$f(x) = 1/x$

domain : all real numbers except $x=0$

$g(x) = \sqrt {x + 2}$

domain : $x$ is greater than or equal to $2$

I'm supposed to find the $f(g(x))$ and $g(f(x))$. This is simple enough, I do not need help with this. What I DO need help with is finding the domain of the composite function.

$f(g(x)) = 1/\sqrt{ x + 2}$

would the domain be all real numbers except $x > -2$?

$g(f(x)) = \sqrt {1/x + 2}$

would the domain be all real numbers except $x > 0$?

the domains from $f(x)$ and $g(x)$ can't help me at all as if I let anything BUT $0$ be the domain I could have a negative square root and that isn't right.

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for $\displaystyle \frac1{\sqrt{x +2}}$ denominator $\neq0$, so $x\neq-2$, also value under sqrt must be positive or zero, $x\geq-2$, combining both $x>-2$ fpr $\displaystyle \sqrt{\frac1x+2}$, value under sqrt must be positive or zero, also x cnnot be zero in denominator, $x\neq0$, domain $x\geq-1/2,x\neq0$

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