Answer
The value of $\left( \frac{g}{f} \right)\left( 3 \right)$ is $0$.
Work Step by Step
Curve ${{C}_{1}}$ represents the values of the function $f\left( x \right)$ and curve ${{C}_{2}}$ represents the values of the function $g\left( x \right)$.
To calculate the value of $\left( \frac{g}{f} \right)\left( 3 \right)$:
Recall that:
$\left( \frac{g}{f} \right)\left( x \right)=\frac{g\left( x \right)}{f\left( x \right)}$ …… (I)
Therefore, the value of $f\left( 3 \right)=-3$ and $g\left( 3 \right)=0$
Apply the equation (I),
$\begin{align}
& \left( \frac{g}{f} \right)\left( 3 \right)=\frac{g\left( 3 \right)}{f\left( 3 \right)} \\
& =\frac{0}{-3} \\
& =0
\end{align}$
Hence, the value of $\left( \frac{g}{f} \right)\left( 3 \right)$ is $0$.
