The image contains some functional compositions and inverse functions, particularly focusing on combinations of functions $f$, $g$, and their inverses. Let me transcribe and explain the key parts:

1. $(f \circ g)(x) = f(g(x))$

   • This is the standard notation for the composition of two functions. It means applying the function $g$ to $x$, then applying $f$ to the result.

2. $(g \circ f)(x) = g(f(x))$

   • Similarly, this is the composition of $g$ and $f$, where $f(x)$ is computed first and then the result is passed to $g$.

3. $(f \circ g)^{-1}(x) = g^{-1}(f^{-1}(x))$

   • This equation shows the inverse of the composition of functions. It follows the rule: to invert a composition of functions, you reverse the order and take the inverse of each function.

4. $f(g(x)) = f \circ g$

   • This again represents the composition of $f$ and $g$, expressed in a slightly different form.

5. $F(2-3)$ and $F(3)$

   • These expressions likely represent specific values being plugged into a function $F$, although it’s not fully clear from the context what $F$ represents.

6. $(f \circ g)(c)$

   • This indicates the composition of $f$ and $g$ applied to a constant $c$.

Would you like further clarification on one of these parts or a detailed step-by-step explanation of any specific equation?

Here are five related questions that may help deepen your understanding:

1. How do we find the inverse of a function, and what does it mean geometrically?
2. Why does the order of operations reverse when taking the inverse of a composition?
3. Can every function have an inverse? If not, what are the conditions for a function to be invertible?
4. What is the significance of function composition in real-world applications?
5. How do we solve equations involving compositions of functions?

Tip: When dealing with compositions and inverses, always pay attention to the order of operations as it plays a critical role in both solving and simplifying equations.