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I can help solve these problems from the image step by step. Let's begin by addressing each one individually:

### Problem 11
We are given that \( f^{-1}, g^{-1}, h^{-1} \) are the inverse functions of \( f, g, h \), respectively, and:
\[
(f^{-1} \circ g^{-1} \circ h^{-1})(x) = 2x - 4
\]
and 
\[
(h \circ g \circ f)(x) = \frac{x-3}{2x+1}, \quad x \neq -\frac{1}{2}.
\]
We are asked to find the value of \( f(8) \).

This problem requires finding the direct functions for \( f, g, h \), and applying the inverse relations to find \( f(8) \).

---

### Problem 12
We are given that \( f \) and \( g \) are functions with inverses, and \( f(g(x)) = 2x - 1 \), and \( g(x+1) = x - 3 \). We are asked to find the value of \( f^{-1}(3) \times g^{-1}(3) \).

First, solve for the inverse functions \( f^{-1} \) and \( g^{-1} \), and then find the required product.

---

### Problem 13
We are given:
\[
f\left( \frac{1}{x+3} \right) = 3x + 4 \quad \text{and} \quad g(x) = x + 4.
\]
We are asked to determine \( (f \circ g)^{-1}(x) \).

This involves finding the composition \( f(g(x)) \), then solving for the inverse of that composition.

---

### Problem 14
We are given:
\[
f^{-1}(x) = \frac{x}{x^2 + 2} \quad \text{and} \quad g^{-1}(x) = \frac{2}{3x},
\]
and are asked to find \( (f \circ g)(2) \).

This can be solved by first finding \( g(2) \), and then substituting into \( f(g(2)) \).

---

### Problem 15
We are given:
\[
f(x) = 2x - 5, \quad g^{-1}(x) = \frac{x+3}{4}, \quad h^{-1}(x) = 8x,
\]
and are asked to find the value of \( (f \circ g \circ h)^{-1}(-7) \).

This problem requires calculating the composition of the inverse functions.

---

### Problem 16
We are given:
\[
f(x - 3) = 6x - 11 \quad \text{and} \quad g(x+1) = \frac{2x-6}{3x+4},
\]
and are asked to find the composition of \( (f \circ g)(2a + 3) \).

This problem requires determining the functions and evaluating the composition at the given expression.

---

### Problem 17
We are given:
\[
f(x) = \frac{2}{x^2 - 2x - 8} \quad \text{and} \quad g(x) = 2x,
\]
and are asked to find the domain of the function \( (f \circ g)(x) \).

This involves finding the composite function and determining its domain.

---

Would you like to proceed with solving each of these step by step starting with Problem 11? Let me know if you'd prefer further clarification on any of the problems!

Solve a series of problems related to inverse functions and function compositions from questions 11-17. Topics include the inverse function theorem, algebraic manipulation, and determining the domain of composite functions.

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