Answer
See the explanation below.
Work Step by Step
To determine the type of function, substitute x by –x and compare it with f(x) as follows:
If $f\left( -x \right)=f\left( x \right)$ , then the function is even.
For example:
$\begin{align}
& \text{Let, }f\left( x \right)={{x}^{2}}+2 \\
& f\left( -x \right)={{\left( -x \right)}^{2}}+2 \\
& f\left( -x \right)={{x}^{2}}+2 \\
& f\left( x \right)=f\left( -x \right)
\end{align}$
If $f\left( -x \right)=-f\left( x \right)$ , then the function is odd.
$\begin{align}
& \text{Let, }f\left( x \right)={{x}^{3}} \\
& \text{ }f\left( -x \right)={{\left( -x \right)}^{3}} \\
& f\left( -x \right)=-{{\left( x \right)}^{3}} \\
& f\left( x \right)=f\left( -x \right)
\end{align}$
If $f\left( -x \right)\ne f\left( x \right)$ , then the function is neither even nor odd.
