if I am ask to get the domain and range of this $\displaystyle y=\frac{2}{\sqrt{x^2+8x+10}}$ how should I start?
Use the definition of domain and range to start your work.
The "domain", being the allowable x-values, will be the values that do not cause division by zero or negatives inside square roots. So you'd set the argument of the radical "greater than or equal to zero", and then solve the quadratic inequality.
The "range" is all the output values, which is often found from the graph. (You don't show any work or say at what level you're studying, so we don't know what other tools you might be able to use.)
Not "equal to 0". That would make the denominator equal to zero.
, and then solve the quadratic inequality.
The "range" is all the output values, which is often found from the graph. (You don't show any work or say at what level you're studying, so we don't know what other tools you might be able to use.)