Let f be the function defined by f(x) = `{((x^2-4)/(x-2),x ne 2), (1, x = 2):}`
Which of the following statement about f is true ?
(a) f is undefined at x = 2
(b) f is continuous at x = 2
(c ) f is discontinuous at x= 2
(d ) f is differentiable at x = 2

Explanation

To determine the continuity of the function \( f(x) \) at \( x = 2 \), we need to analyze the function defined as follows:

\[
f(x) =
\begin{cases}
\frac{x^2 - 4}{x - 2} & \text{if } x \neq 2 \\
1 & \text{if } x = 2
\end{cases}
...