When looking at a rational function f of x equals the quantity x plus three times the quantity x minus two times the quantity x plus five all divided by the quantity x minus three times the quantity x plus two times the quantity x minus 5, Charles and Bobby have two different thoughts. Charles says that the function is defined at x = - 2, x = 3, and x = 5. Bobby says that the function is undefined at those x values. Who is correct? Justify your reasoning.

Question

Coby Casey

Mathematics

Today, 12:31

When looking at a rational function f of x equals the quantity x plus three times the quantity x minus two times the quantity x plus five all divided by the quantity x minus three times the quantity x plus two times the quantity x minus 5, Charles and Bobby have two different thoughts. Charles says that the function is defined at x = - 2, x = 3, and x = 5. Bobby says that the function is undefined at those x values. Who is correct? Justify your reasoning.

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Answers (1)

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Jaydan Levy · Answer 1

Bobby is correct

Step-by-step explanation:

∵ f (x) is undefined for all values of x make the denominator = 0

∵ The denominator = (x - 3) (x + 2) (x - 5)

∵ x - 3 = 0 ⇒ x = 3

∵ x + 2 = 0 ⇒ x = - 2

∵ x - 5 = 0 ⇒ x = 5

∴ f (x) is undefined if x = - 2, x = 3, x = 5

∴ The domain of f (x) is all the real number except - 2, 3, 5