# What is the domain and range of f(x) =sqrt(28.5 − 3 x)?

Jan 5, 2018

Domain: $\left(- \infty , 9.5\right]$
Range: $\left[0 , + \infty\right)$

#### Explanation:

The condition of existence of a square root is satisfied for the radicand$\setminus \ge 0$.

So let's solve:
$28.5 - 3 x \setminus \ge 0$
$- 3 x \setminus \ge - 28.5$
$3 x \setminus \le 28.5$
$\setminus \frac{3}{3} x \setminus \le \setminus \frac{28.5}{3}$
$x \setminus \le 9.5$

Domain: $\left(- \infty , 9.5\right]$

While the range is positive for every $x \setminus \in \left(- \infty , 9.5\right]$ that you put in $f \left(x\right)$.

Range: $\left[0 , + \infty\right)$

graph{sqrt(28.5-3x) [-2.606, 11.44, -0.987, 6.04]}