Question

How do you find the domain and range of `y= 1 / (x-3)`?

Answer 1

Domain `= {x:x epsilon RR, x != 3}`
Range `y ={y:y epsilon RR, y!= 0}`

Explanation:

The domain is the set of all the x-values.

We notice that `x` is in the denominator, and the only restriction for a denominator is that it may not be equal to 0.
If `x - 3 = 0 rArr x =3`

So `x` can have any value except 3.

This equation can also be written as `(x - 3) = 1/y`
The range is the set of all the `y` values

In this case we can see that `y` may not be equal to 0

So `y` can have any value except 0.

Domain `= {x:x epsilon RR, x != 3}`
Range `y ={y:y epsilon RR, y!= 0}`