Chapter 1.2, Problem 28E

To determine

To check: Whether the function $y=\sqrt[3]{2-x}$ is even, odd or neither.

Answer to Problem 28E

The function $y=\sqrt[3]{2-x}$ is neither even nor odd function.

Explanation of Solution

Given information: The function is $y=\sqrt[3]{2-x}$.

Rewrite the function.

  $\begin{array}{l}y=\sqrt[3]{2-x}\\ y=\sqrt[3]{2x^0-x}\end{array}$

The function $y=\sqrt[3]{2-x}$ is the addition of odd and even powers of $x$.

Therefore, the function $y=\sqrt[3]{2-x}$ is neither even nor odd function.