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

1 Answer
Jan 5, 2018

Answer:

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]}