How to find the domain and range of $f(x) = \sqrt {\frac{x+1}{x+2}}$ 
Find the domain and range of $$f(x) = \sqrt {\frac{x+1}{x+2}}$$

I got the domain $[-1, \infty)$ but the answer contains $(-\infty, -2)$ along with it. And how to calculate range?

The sign of $\dfrac{x+1}{x+2}$ is the same as the sign of $(x+1)(x+2)$. The latter is a parabola with positive concavity  and roots at $-2$ and $-1$ therefore is positive for $x < -2$ or $x>-1$.
In your case $x=-1$ allowed while $x=-2$ is not. So the domain you are looking for is $(-\infty,-2) \cup [-1,\infty)$.
