## Precalculus (6th Edition) Blitzer

The value of $\left( \frac{g}{f} \right)\left( 3 \right)$ is $0$.
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 $0$.