Let be some fixed parameter. The following function is discontinuous at .Question 5Select one:TrueFalse

To determine whether the function is discontinuous at a specific point, we need to consider conditions of continuity. A function is continuous at a point $c$ if the following three conditions hold:

1. The function $f(c)$ is defined.
2. The limit of the function as it approaches $c$, $\lim_{x \to c} f(x)$, exists.
3. The limit equals the function value, i.e., $\lim_{x \to c} f(x) = f(c)$.

If any of these conditions fail, the function is deemed discontinuous at that point.

Step-by-step Analysis:

1. Identify the point $c$ at which we are checking discontinuity.
2. Check if $f(c)$ is defined:
   • If it is not defined, the function is discontinuous at $c$.
3. Evaluate $\lim_{x \to c} f(x)$:
   • If this limit does not exist or equals a different value than $f(c)$, the function is discontinuous at $c$.
4. Conclude based on these findings.

Conclusion:

Without the specific function or value of $c$, we cannot definitively determine if the statement is true or false. However, if the conditions for continuity are violated, the correct answer would be True indicating the function is discontinuous at $c$. If all conditions are satisfied, then the answer would be False.

Thus, without additional information about the function and its discontinuity point, I cannot provide a precise answer. But based on the general principles of continuity, I can confirm that the assessment of the function at the specific point will indicate whether it is indeed discontinuous.