Question

How do you find the domain and range of `f(x) = 2 / sqrt(3x-2)`?

Answer 1

The domain is `{x:x in R and x>2/3}` and the range is `{y:y in R and y>0}`

Explanation:

The domain is the set of values which can be passed into a function. In this case, we have the constraint:

`3x-2>=0` (since you can't have a root of a negative number)

`3x>2`
`x>2/3`

Hence, the domain is `{x:x in R and x>2/3}`

The range is the set of values which the function can produce. As `x` increases, the value of the root gets larger and `f(x)` tends towards `0`. Hence the range is `{y:y in R and y>0}`