Chapter 3, Problem 4CT

To determine

The value of $x$ is to be calculated with $f\left(x\right)=g\left(x\right)$ and draw each function with intersection point by using the following functions:

  $\begin{array}{l}f\left(x\right)=x^2+3x\\ g\left(x\right)=3x+3\end{array}$

Answer to Problem 4CT

The solution $f\left(x\right)=g\left(x\right)$ is $\pm \sqrt{3}$ . And the graph is drawn as:

  

Explanation of Solution

Given:

  $\begin{array}{l}f\left(x\right)=x^2+3x\\ g\left(x\right)=3x+3\end{array}$

Calculation:

The quadratic equations are given as:

  $\begin{array}{l}f\left(x\right)=x^2+3x\\ g\left(x\right)=3x+3\end{array}$

Now, solve for $f\left(x\right)=g\left(x\right)$ :

  $\begin{array}{l}f\left(x\right)=g\left(x\right)\\ x^2+3x=3x+3\\ x^2=3\\ x=\pm \sqrt{3}\end{array}$

The graph of both functions and their intersection point is labelled in the following image:

  

Conclusion:

Hence, the point of intersection of $f\left(x\right)=x^2+3x$ and $g\left(x\right)=3x+3$ is $G\left(3,8\right)$ .