Question

the graph of the function f is shown above. what are all values of x for which f has a removable discontinuity?

Explanation:

Step1: Recall definition of removable discontinuity

A removable discontinuity occurs when the limit of the function exists at a point, but the function is not continuous there (either not - defined or has a different value).

Step2: Analyze the graph

At \(x = 1\), the function has a hole. The limit of \(f(x)\) as \(x\to1\) exists (the left - hand and right - hand limits are equal), but the function is not defined at \(x = 1\). At \(x=6\), the function has a hole. The limit of \(f(x)\) as \(x\to6\) exists (left - hand and right - hand limits are equal), but the function is not defined at \(x = 6\).

Answer:

\(x = 1\) and \(x=6\)