Answer to Question #263093 in Calculus for Sam

Question

Find the domain and range of the following function given by

𝑓(𝑥)=√(3𝑥−5)(𝑥+4)𝑥3−16𝑥.

Answer 1

$$𝑓(𝑥)=\sqrt{(3𝑥−5)(𝑥+4)}𝑥^3−16𝑥$$

$$(3x-5)(x+4)\geq0$$

$$x\leq-4\ or\ x\geq5/3$$

Domain: $(-\infin, -4]\cup [5/3, \infin)$

Range: $(-\infin, \infin)$