Answer
The value of $\left( f\circ g \right)\left( 1 \right)$ is $3$.
Work Step by Step
Consider the above graph:
The curve ${{C}_{1}}$, shows the values of the function $f\left( x \right)$ and curve ${{C}_{2}}$ shows the values of the function $g\left( x \right)$.
The composition of f with g can be defined as the function $\left( f\circ g \right)$ and $\left( f\circ g \right)\left( x \right)$ which is equivalent to $f\left( g\left( x \right) \right)$.
Consider the equation below:
$\left( f\circ g \right)\left( 1 \right)=f\left( g\left( 1 \right) \right)$
Here,
$g\left( 1 \right)=-5$.
Then,
$f\left( g\left( 1 \right) \right)=f\left( -5 \right)$
And the value of $f\left( -5 \right)=3$.
Hence, $\left( f\circ g \right)\left( 1 \right)=3$
Hence, the value of $\left( f\circ g \right)\left( 1 \right)$ is $3$.
