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

Question

1809 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-05T14:14:03

Domain: $(-oo, 9.5]$
Range: $[0, +oo)$

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

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

Domain: $(-oo, 9.5]$

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

Range: $[0, +oo)$

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

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