Draw a neat graph of f(x) and f⁻¹(x) on the same system of axes, clearly showing endpoints and the line of reflection.

I've already provided the solutions for parts 2.3.1 through 2.3.5 in the previous message.

For question 2.3.6, which asks for a graph, I will describe how to draw it, as I cannot directly create an image.

2.3.6 Draw a neat graph of $f(x)$ and $f^{-1}(x)$ on the same system of axes on ADDENDUM A (attached), clearly showing the nature of the start and endpoints on the graphs. Also show the line about which $f(x)$ reflects $f^{-1}(x)$ and label it.

To draw the graph:

• Graph of $f(x) = 2x+3$:

  • The domain for $f(x)$ is $x \in [-1, 2)$.
  • Calculate the starting point: When $x = -1$, $f(-1) = 2(-1) + 3 = 1$. Plot a closed circle at the coordinate $(-1, 1)$ because $x \ge -1$.
  • Calculate the ending point: When $x = 2$, $f(2) = 2(2) + 3 = 7$. Plot an open circle at the coordinate $(2, 7)$ because $x < 2$.
  • Draw a straight line connecting these two points.

• Graph of $f^{-1}(x) = \frac{x-3}{2}$:

  • The domain for $f^{-1}(x)$ is $x \in [1, 7)$, which is the range of $f(x)$.
  • Calculate the starting point: When $x = 1$, $f^{-1}(1) = \frac{1-3}{2} = -1$. Plot a closed circle at the coordinate $(1, -1)$.
  • Calculate the ending point: When $x = 7$, $f^{-1}(7) = \frac{7-3}{2} = 2$. Plot an open circle at the coordinate $(7, 2)$.
  • Draw a straight line connecting these two points.

• Line of reflection:

  • Draw a dashed or solid line representing the equation $y=x$. This line should pass through the origin $(0,0)$ and points like $(1,1)$, $(2,2)$, etc.