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

1 Answer
Azimet
Jan 16, 2017

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].

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