This question involves analyzing the graphs of two functions and finding various properties of them. Let's break down the questions based on the graph and the function given.

Question Breakdown:

1. Coordinates of E (4.1):

   • Point E is the y-intercept of both the parabola $f(x) = (x - 4)^2 - 9$ and the line $g$.
   • To find the coordinates of E, we'll need to substitute $x = 0$ into the equation of $f(x)$ to find the y-coordinate. The x-coordinate will be $0$ because it's the y-intercept.

2. Coordinates of A (4.2):

   • A is the x-intercept of the function $f(x)$, which means we set $f(x) = 0$ and solve for $x$.

3. Reflection of C in the axis of symmetry (4.3):

   • The point M is the reflection of C in the axis of symmetry of the parabola. The axis of symmetry of $f(x)$ is the vertical line passing through the vertex of the parabola, i.e., $x = 4$. To find M, we'll reflect the coordinates of C across this axis.

4. Equation of line g (4.4):

   • From the graph, we can see that line $g$ is a straight line with a slope $m$ and y-intercept $c$. We can find the equation by determining these two values from the graph.

5. Equation of the inverse of g (4.5):

   • Once we have the equation of line $g$, the inverse $g^{-1}$ can be found by swapping the roles of $x$ and $y$, and solving for $y$.

6. For which values of $x$ will $|g(f(x))| \leq 0$ (4.6):

   • This asks for the values of $x$ where the composition $g(f(x))$ is less than or equal to 0. This will involve substituting $f(x)$ into $g(x)$, solving for the x-values where the result is less than or equal to 0.

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