# Thread: domain and range

1. ## domain and range

if I am ask to get the domain and range of this $y=\frac{2}{\sqrt{x^2+8x+10}}$ how should I start?

2. Originally Posted by princess_21
if I am ask to get the domain and range of this $y=\frac{2}{\sqrt{x^2+8x+10}}$ 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.)

3. Originally Posted by stapel
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"
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.)

4. Originally Posted by HallsofIvy
Not "equal to 0". That would make the denominator equal to zero.
Quite.

The "greater than or equal to" solves the square root part. Then one would need to throw out the "or equal to" to prevent the division by zero.

Thank you!