Question

20 Points- Which of the following is true for f of x equals the quotient of the quantity x squared plus 9 and the quantity x minus 3?
There is a removable discontinuity at x = 3.
There is a non-removable discontinuity at x = 3.
The function is continuous for all real numbers.

Answer 1

Answer:

There is a non-removable discontinuity at x = 3

Step-by-step explanation:

We are  given that

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

We have to find true statement about given function.

$\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}$

=$\infty$

It is not removable discontinuity.

x-3=0

x=3

The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.

Therefore, x=3 is non- removable discontinuity of function f(x).

Hence, option B is correct.