Answer to Question #252423 in Calculus for gael

Question #252423

Find the domain and range of the following function given by

𝑓(π‘₯)=√(3π‘₯βˆ’5)(π‘₯+4)/π‘₯3βˆ’16π‘₯


1
Expert's answer
2021-10-18T13:27:37-0400
"f(x)=\\dfrac{\\sqrt{(3x-5)(x+4)}}{x^3-16x}"

"(3x-5)(x+4)\\geq0=>x\\leq-4\\ or\\ x\\geq\\dfrac{5}{3}"

"x^3-16x\\not=0=>x\\not=-4, x\\not=0, x\\not=4"

"Domain: (-\\infin, -4)\\cup[\\dfrac{5}{3}, 4)\\cup(4, \\infin)"

"x\\in (-\\infin, -4), f(x)\\in(-\\infin, 0)"


"x\\in [\\dfrac{5}{3}, 4), f(x)\\in(-\\infin, 0]"


"x\\in (4, \\infin), f(x)\\in(0,\\infin)"



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


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