Question

Multiple Choice Which of the following points is not a point of discontinuity of \(f(x)=\sqrt{x-1} ?\) (A) \(x=-1 \quad\) (B) \(x=-1 / 2 \quad\) (C) \(x=0\) (D) \(x=1 / 2 \quad\) (E) \(x=1\)

Short answer

The point \(x=1\) (Option E) is not a point of discontinuity for the function \(f(x)=\sqrt{x-1}\).

Step-by-step solution

Identify the solved domain of the function

The function \(f(x)=\sqrt{x-1}\) is only defined for \(x \geq 1\). This means the function is continuous for \(x \geq 1\). Therefore, any value that is less than 1, is a point of discontinuity for this function.

Evaluate the given options for the definition of the function

Among the given options, all values of x are less than 1, except for option E that is \(x=1\). Since \(x=1\) falls in the solved domain of the function \(\sqrt{x-1}\), this value does not represent a discontinuity of the function.