Chapter 2.3, Problem 57E

To determine

To find: The correct choice for point at which the function $f\left(x\right)=\sqrt{x-1}$ is not discontinuous.

Answer to Problem 57E

The correct choice is (E).

Explanation of Solution

Given information: The function is $f\left(x\right)=\sqrt{x-1}$.

Check the continuity of the function $f\left(x\right)=\sqrt{x-1}$ with the help of graph.

To graph a function $y=\sqrt{x-1}$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{Y}=}$ key and enter right hand side of the equation $y=\sqrt{x-1}$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{2\text{nd}}\boxed{x^2}\boxed{\text{X}}\boxed{-}\boxed{1}\boxed{)}$.

The display will show the equation,

  ${\text{Y}}_{\text{1}}=\sqrt{\text{X}-1}$

Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of given function in standard window as shown below.

  

Figure (1)

As observed from graph, the function $f\left(x\right)=\sqrt{x-1}$ is continuous at every point $x\ge 1$ . So, the function $f\left(x\right)=\sqrt{x-1}$ is not discontinuous at $x=1$.

Therefore, the correct choice is (E).