Chapter 1.3, Problem 6E

To determine

The points of discontinuity of the function. Identify the type of

Discontinuity.

Answer to Problem 6E

The function is continuous everywhere and has no point of discontinuity.

Explanation of Solution

Given:

  $y=\sqrt[3]{2x-1}$

Calculation:

The given equation $y=\sqrt[3]{2x-1}$ is a composition of two functions, $f\left(x\right)=\sqrt[3]{x}$ and $g\left(x\right)=2x-1$ . Both, the functions are continuous. So, the function is continuous.

Find the discontinuity point of the function$y=\sqrt[3]{2x-1}$:

The function is continuous and its domain is $\left(-\infty ,\infty \right)$ .

Thus, the domain of the expression is all real numbers except where the expression is

undefined. In this case, there is no real number that makes the expression undefined.

Thus, the function is continuous everywhere and has no point of discontinuity.