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It looks like you've uploaded a photo containing a set of mathematical problems involving functions and compositions of functions. Let's go through some of the key problems and solutions.

### Problem 16: 
Given:
- \( f: \mathbb{R} \to \mathbb{R} \)
- \( g: \mathbb{R} \to \mathbb{R} \)
- \( g(x) = 3x + 1 \)
- \( (f \circ g)(x) = x^2 + 3 \)

Find \( f(2x - 4) \).

To solve, we first need to determine \( f(x) \) using the equation for \( (f \circ g)(x) \).

\[
(f \circ g)(x) = f(g(x)) = f(3x + 1) = x^2 + 3
\]

Thus, \( f(y) = \left(\frac{y - 1}{3}\right)^2 + 3 \), where \( y = 3x + 1 \).

Substitute \( y = 2x - 5 \) into this formula, and simplify to get \( f(2x - 4) \).

### Problem 17:
We are given:
- \( f(x) = 3x^2 - 4x + 6 \)
- \( g(x) = 2x - 1 \)
- \( (f \circ g)(x) = 101 \)

We are tasked with finding \( x \).

Using the composition \( (f \circ g)(x) = f(g(x)) \), we substitute \( g(x) = 2x - 1 \) into \( f(x) \):

\[
f(2x - 1) = 101
\]

Solve for \( x \).

### Problem 18:
Given:
- \( f(x) = x^2 - x \)
- \( g(x) = 2x + 3 \)
- \( h(x) = 1 - 3x \)

Find \( (f \circ g \circ h)(x) \), which involves evaluating \( f(g(h(x))) \).

First, calculate \( h(x) \), substitute into \( g(x) \), then substitute the result into \( f(x) \).

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Would you like more detailed solutions to any specific problems, or should I continue solving others from the image? 

Here are five follow-up questions based on the problems:
1. How do you find the composition of two functions, \( f(g(x)) \)?
2. What is the step-by-step process for solving \( (f \circ g)(x) = 101 \)?
3. How do you simplify complex expressions involving function compositions like \( f(g(h(x))) \)?
4. How can you derive \( f(x) \) from \( (f \circ g)(x) \)?
5. What techniques are helpful when solving quadratic equations in function problems?

**Tip**: Always break down compositions of functions step by step to avoid errors, starting from the innermost function and working outward.

Given the functions f(x) = 3x^2 - 4x + 6 and g(x) = 2x - 1, if (f o g)(x) = 101, what is the value of x?

Learn how to solve a function composition problem where f(x) = 3x^2 - 4x + 6 and g(x) = 2x - 1. The task is to find the value of x such that (f o g)(x) = 101. This problem involves algebraic techniques and quadratic equations, suitable for Grades 10-12.

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