For a function to be even, it has to meet this condition:
[tex]f(x)=f(-x)[/tex]To check if the given is an even function, find f(x) and f(-x) and see if they are equal:
[tex]\begin{gathered} f(x)=5-3x \\ f(-x)=5-3(-x)=5+3x \end{gathered}[/tex]In this case, the function is not even.
For a function to be odd, it has to meet this condition:
[tex]f(-x)=-f(x)[/tex]We already know that f(-x)=5+3x. Let's find -f(x):
[tex]\begin{gathered} f(x)=5-3x \\ -f(x)=-5+3x \end{gathered}[/tex]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.
