Question

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

Answer 1

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

Explanation:

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]}