Question

Determine algebraically if f(x)=5-3x is a function even, odd, or neither.

Answer 1

For a function to be even, it has to meet this condition:

$f(x)=f(-x)$

To check if the given is an even function, find f(x) and f(-x) and see if they are equal:

$\begin{gathered} f(x)=5-3x \\ f(-x)=5-3(-x)=5+3x \end{gathered}$

In this case, the function is not even.

For a function to be odd, it has to meet this condition:

$f(-x)=-f(x)$

We already know that f(-x)=5+3x. Let's find -f(x):

$\begin{gathered} f(x)=5-3x \\ -f(x)=-5+3x \end{gathered}$

According to this -f(x) is not equal to f(-x), which means that the function is not odd neither.

The answer is that the function is not even nor odd.