Question

How do you find the domain and range of `sqrt(6x-30)`?

Answer 1

The domain is `A = [5, +infty)`

The range is `B = [0, +infty)`

Explanation:

To find the domain, find the set, or interval, that contains all values of `x` for which `sqrt(6x - 30)` makes sense.

We see that, since `sqrta` is only defined if `a >= 0`, this must apply:

`6x - 30 >= 0 => 6x >= 30 => x >= 5`.

Therefore, the domain is the interval `[5, +infty]`.

Finding the range of this function is not as tricky as others: for any real `x`, which can take any real value, `6x` can also take any real value and so can `6x-30`. Thus, `6x-30` can definitely take any non-negative real value. Since square roots only accept non-negative numbers and their output is also non-negative, we see that the range is all non-negatives, or the interval `[0, +infty]`.