Question

Explain why f(x) is continuous at x=3

Answer 1

f is not defined at x = 3 ⇒ answer (b)

Explanation:

∵ f(x) = x² - x - 6/x² - 9 is a rational function

∴ It will be undefined at the values of x of the denominator

∵ The denominator is x² - 9

∵ x² - 9 = 0 ⇒ x² = 9 ⇒ x = ±√9

∴ x = ± 3

∴ f(x) can not be defined at x = 3

∴ The f(x) can not be continuous at x = 3

∴ The answer is (b)

Answer 2

b. f is not defined at x=3

Explanation:

The given function is

`f(x)=(x^2-x-6)/(x^2-9)`

One of the conditions for continuity is that; the function must be defined at
`x=a`

If we plug in
`x=3`, we obtain;

`f(x)=(3^2-3-6)/(3^2-9)`

`f(x)=(9-3-6)/(9-9)`

`f(x)=(0)/(0)`

Since the function is not defined at x=3, it is not also continuous at x=3

The correct choice is B