Question

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.

Answer 1

Bobby is correct

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