Answer
The values are \[f\left( 2 \right)=-1\] and \[f\left( 3 \right)=16\]
Work Step by Step
To find $f\left( 2 \right)$ in the given function, replace $x=2$ in the provided equation:
$\begin{align}
& f\left( 2 \right)={{2}^{3}}-2\left( 2 \right)-5 \\
& =8-9 \\
& =-1
\end{align}$
To find $f\left( 3 \right),$ replace $x=3$ in the given equation:
$\begin{align}
& f\left( 3 \right)={{3}^{3}}-2\left( 3 \right)-5 \\
& =27-11 \\
& =16
\end{align}$
Since, $f\left( 2 \right)$ is negative and $f\left( 3 \right)$ is positive and the function is continuous, thus to go from $f\left( 2 \right)$ to $f\left( 3 \right)$ , the curve must cross the x-axis.
Hence, the values are $f\left( 2 \right)=-1$ and $f\left( 3 \right)=16$.
