[tex]f(x)=5-3x \\
x \in \mathbb{R}[/tex]
A function is even if f(x)=f(-x) for every x in the domain.
[tex]f(x) \stackrel{?}{=} f(-x) \\
5-3x \stackrel{?}{=} 5-3 \times (-x) \\
5-3x \stackrel{?}{=} 5+3x \\
-3x-3x \stackrel{?}{=} 5-5 \\
-6x \stackrel{?}{=} 0 \\
x \stackrel{?}{=} 0 \\
f(x)=f(-x) \Leftrightarrow x=0[/tex]
f(x) is equal to f(-x) if and only if x=0, so the function isn't even.
A function is odd if -f(x)=f(-x) for every x in the domain.
[tex]-f(x) \stackrel{?}{=} f(-x) \\
-(5-3x) \stackrel{?}{=} 5-3 \times (-x) \\
-5+3x \stackrel{?}{=} 5+3x \\
3x-3x \stackrel{?}{=} 5+5 \\
0 \stackrel{?}{=} 10 \\
0 \not= 10 \\
-f(x) \not= f(-x)[/tex]
-f(x) is never equal to f(-x), so the function isn't odd.
The function is neither even nor odd.
