Chapter 1.3, Problem 85E

(a)

To determine

Whether the given function is even or odd or does not satisfy either condition

Answer to Problem 85E

The given function is neither even nor odd.

Explanation of Solution

Given information:

The function $f(x)=4-x$

Formula used:

A function is even if it satisfies the condition $f(x)=f(-x)$ . If it satisfies the condition $f(x)=-f(-x)$ , it is odd.

Calculation:

Consider the function $f(x)=4-x$ . The function $f(-x)$ is given by,

  $\begin{array}{c}f(-x)=4-\left(-x\right)\\ =4+x\end{array}$

It can be seen that, the $f(x)$ does not satisfy the property of even and odd functions. Hence it is neither even nor odd function.

b.

To determine

Whether the given function is even, odd or none.

Answer to Problem 85E

The function is neither even nor odd.

Explanation of Solution

Given information:

The function $f(x)=4-x$

Graph:

The given function is sketched as shown below.

  

Interpretation:

From the graph, it can be seen that the given function represents a straight line which is neither symmetric nor antisymmetric. Thus, the given function is neither even nor odd.

c.

To determine

Whether the given function is even, odd or none.

Answer to Problem 85E

The function is neither even nor odd.

Explanation of Solution

Given information:

The function $f(x)=4-x$

The values of the given function for different values of x are shown in the below table.

  

From the table, it can be observed that, for all the values of x considered, the function $f(x)\ne f(-x)$ and $f(x)\ne -f(-x)$ . Hence the given function is neither even nor odd.