Question

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

Answer 1

Answer:

b. f is not defined at x=3

Step-by-step explanation:

The given function is

$f(x)=\frac{x^2-x-6}{x^2-9}$

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

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

$f(x)=\frac{3^2-3-6}{3^2-9}$

$f(x)=\frac{9-3-6}{9-9}$

$f(x)=\frac{0}{0}$

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

The correct choice is B

Answer 2

Answer:

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

Step-by-step 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)