$\text { Discuss the continuity of the function } f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 } \text {. }$

Question

Quizplus · Accepted Answer

The function has a removable singularity at x = 2. We can simplify the function as follows:
$$f(x) = \frac{x^2-4}{x-2} = \frac{(x-2)(x+2)}{x-2}= x+2, \ 	ext{ for } x
eq 2.$$ 
Thus, the limit of the function as x approaches 2 is 4. However, at x = 2, the function is undefined since we can't divide by zero. Therefore, the function is discontinuous at x = 2. It is continuous everywhere else.

Discuss the continuity of the function f(x)=x2−4x−2. \text { Discuss the continuity of the function } f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 } \text {. } Discuss the continuity of the function f(x)=x−2x2−4​.

$\text { Discuss the continuity of the function } f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 } \text {. }$