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

Jan 16, 2017

The domain is $A = \left[5 , + \infty\right)$

The range is $B = \left[0 , + \infty\right)$

#### Explanation:

To find the domain, find the set, or interval, that contains all values of $x$ for which $\sqrt{6 x - 30}$ makes sense.

We see that, since $\sqrt{a}$ is only defined if $a \ge 0$, this must apply:

$6 x - 30 \ge 0 \implies 6 x \ge 30 \implies x \ge 5$.

Therefore, the domain is the interval $\left[5 , + \infty\right]$.

Finding the range of this function is not as tricky as others: for any real $x$, which can take any real value, $6 x$ can also take any real value and so can $6 x - 30$. Thus, $6 x - 30$ 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 $\left[0 , + \infty\right]$.