Answer
The value of $\left( f\circ f \right)\left( -1 \right)$ is $3$.
Work Step by Step
$\left( f\circ f \right)$ is defined as the composition of f with f.
$\left( f\circ f \right)\left( x \right)=f\left( f\left( x \right) \right)$
Here, substitute x with $f\left( x \right)$ in the expression of the function.
In order to find the value of $\left( f\circ f \right)\left( -1 \right)=f\left( f\left( -1 \right) \right)$ , first find the value of $f\left( -1 \right)$.
It has been observed that $x=-1$ is a zero of the function.
Thus, $f\left( -1 \right)=0$.
Substitute the value of $f\left( -1 \right)$ in $f\left( f\left( -1 \right) \right)$.
$f\left( f\left( -1 \right) \right)=f\left( 0 \right)$
Also, $f\left( 0 \right)=3$.
$\begin{align}
& \left( f\circ f \right)\left( -1 \right)=f\left( f\left( -1 \right) \right) \\
& =f\left( 0 \right) \\
& =3
\end{align}$
Therefore, the value of $\left( f\circ f \right)\left( -1 \right)$ is $3$.
