How do you find the domain and range of #y =sqrt(x-2) / (6+x)#?
You need to ensure that:
1] the denominator is different from zero, so:
2] the argument of the square root must be bigger or equal to zero, so:
These conditions are used to avoid points or intervals where your function cannot be calculated.
Finally the domain is all real
For the range I evaluated the maximum through the derivative:
The maximum is at