Question 1113891

Replace {{{x}}} with {{{-x}}} and compare the result to {{{f(x)}}}.
If {{{f(-x) = f(x)}}}, the function is {{{even}}}.
If {{{f(-x) = - f(x) }}}, the function is {{{odd}}}.
If {{{f(-x) <> f(x) }}} and {{{f(-x) <> -f(x) }}}, the function is {{{neither }}}{{{even }}}{{{nor}}}{{{ odd}}}.

Remember that {{{(-x)^n=x^n}}} if {{{n}}} is even, and {{{(-x)^n=-x^n}}} if {{{n}}} is odd

So, in your case we have:
a.	{{{f(x) = 5x ^3 - 2x}}} … replace {{{x}}} with {{{-x}}}
{{{f(-x) = 5(-x) ^3 -2(-x)}}}
{{{f(-x) = -5x^3 +2x}}} …..since {{{f(-x) = - f(x) }}}, the function is {{{odd}}}

b. 

{{{f(x) = x ^2 + 3x - 2}}}
{{{f(-x) = (-x )^2 + 3(-x) - 2}}}
{{{f(x) = x ^2 -3x - 2}}}….since {{{f(-x) <> f(x) }}} and {{{f(-x) <> -f(x) }}}, the function is {{{neither }}}{{{even }}}{{{nor}}}{{{ odd}}}.