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You’ve provided two images. The first image defines four functions, and the second image presents a composition of functions question. Let’s break it down:

### Functions provided:
1. \( f(x) = \frac{3}{2}x + 1 \)
2. \( g(x) = x^2 - 5x \)
3. \( h(x) = \frac{2x - 1}{33} \)
4. \( j(x) = 3x + 1 \)

### Question:
Find \( (f \circ g)(x) \), which means the composition of \( f(x) \) and \( g(x) \), or in simpler terms, \( f(g(x)) \).

### Solution:
To find \( (f \circ g)(x) = f(g(x)) \), we substitute \( g(x) \) into \( f(x) \).

1. Recall:
   \[
   f(x) = \frac{3}{2}x + 1
   \]
   So, to compute \( f(g(x)) \), replace \( x \) in \( f(x) \) with \( g(x) \), which is \( x^2 - 5x \).

2. Substitution:
   \[
   f(g(x)) = \frac{3}{2}(x^2 - 5x) + 1
   \]

3. Now, distribute the \( \frac{3}{2} \) to each term inside the parentheses:
   \[
   f(g(x)) = \frac{3}{2}x^2 - \frac{15}{2}x + 1
   \]

Thus, the final expression for \( (f \circ g)(x) \) is:
\[
(f \circ g)(x) = \frac{3}{2}x^2 - \frac{15}{2}x + 1
\]

Would you like a further explanation or to go through additional examples?

### 5 Related Questions:
1. What is \( (g \circ f)(x) \)?
2. How do you find \( (h \circ j)(x) \)?
3. What happens if you compose \( f(x) \) with itself, \( (f \circ f)(x) \)?
4. How would you solve \( f(g(2)) \)?
5. How do you find the inverse of the function \( f(x) \)?

### Tip:
When composing functions, always substitute one function into the other carefully, and simplify step by step to avoid errors.

Find (f ∘ g)(x) based on the given functions: f(x) = (3/2)x + 1 and g(x) = x^2 - 5x.

Learn how to solve function composition problems such as (f ∘ g)(x) where f(x) = (3/2)x + 1 and g(x) = x^2 - 5x. This step-by-step guide covers essential algebraic concepts and is suitable for high school students (Grades 10-12).

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