The domain of a function is all possible values of x where f(x) is defined. Here, when the denominator is equal to 0, the function is undefined. In this case:
x+6=0
x=-6
So y is only undefined at x=-6. In interval notation, we write the domain as (-oo,-6)uu(-6,oo).
The range of a function is all possible values for y. Another way to solve for the range is to find y^-1, as in, the inverse function of y, and find its domain. Here, we can find y^-1:
y=3/(x+6)
Switch the variables and solve for y:
x=3/(y+6)
1/x=(y+6)/3
3/x=y+6
y=3/x-6
This is y^-1. It is also defined when its denominator is equal to 0.
So y^-1 will be undefined when x=0, and therefore y will be undefined when y=0. The range in interval notation is:
(-oo,0)uu(0,oo)
