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

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)
Answer:
b. f is not defined at x=3
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{x^2-x-6}{x^2-9}[/tex]
One of the conditions for continuity is that; the function must be defined at [tex]x=a[/tex]
If we plug in [tex]x=3[/tex], we obtain;
[tex]f(x)=\frac{3^2-3-6}{3^2-9}[/tex]
[tex]f(x)=\frac{9-3-6}{9-9}[/tex]
[tex]f(x)=\frac{0}{0}[/tex]
Since the function is not defined at x=3, it is not also continuous at x=3
The correct choice is B