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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