Chapter 1.2, Problem 29E

To determine

To check: Whether the function $y=\frac{1}{x-1}$ is even, odd or neither.

Answer to Problem 29E

The function $y=\frac{1}{x-1}$ is neither even nor odd function.

Explanation of Solution

Given information: The function is $y=\frac{1}{x-1}$.

Calculation:

Rewrite the function.

  $\begin{array}{l}y=\frac{1}{x-1}\\ y=\frac{x^0}{x-x^0}\end{array}$

The function $y=\frac{1}{x-1}$ is the quotient of even power to the subtraction of even and odd powers of $x$.

Therefore, the function $y=\frac{1}{x-1}$ is neither even nor odd function.