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I have opened the image. Let's begin by solving the provided problems step by step.

### 1. Diketahui bahwa:
\( f(x) = 3x - 8 \)  
\( g(x) = 2x^2 - 5x + 3 \)  
\( h(x) = \frac{2x + 5}{x - 1} \)  
\( i(x) = \frac{-5}{2x + 3} \)

Now, we will proceed with solving each part of the first question.

#### a. \((f + g)(x)\)
\[
(f + g)(x) = f(x) + g(x) = (3x - 8) + (2x^2 - 5x + 3) = 2x^2 - 2x - 5
\]

#### b. \( (2f - g + 3h)(x) \)
\[
(2f - g + 3h)(x) = 2f(x) - g(x) + 3h(x)
\]
First, calculate each term:
\[
2f(x) = 2(3x - 8) = 6x - 16
\]
\[
g(x) = 2x^2 - 5x + 3
\]
\[
3h(x) = 3\left(\frac{2x + 5}{x - 1}\right) = \frac{6x + 15}{x - 1}
\]
Now combine them:
\[
(6x - 16) - (2x^2 - 5x + 3) + \frac{6x + 15}{x - 1}
\]

#### c. \( g(x) \cdot i(x) \)
\[
g(x) \cdot i(x) = (2x^2 - 5x + 3) \cdot \left(\frac{-5}{2x + 3}\right)
\]

#### d. \( \frac{h(x)}{g(x)} \)
\[
\frac{h(x)}{g(x)} = \frac{\frac{2x + 5}{x - 1}}{2x^2 - 5x + 3}
\]

#### e. \( (f \circ g)(x) \)
This is the composition \( f(g(x)) \):
\[
f(g(x)) = f(2x^2 - 5x + 3) = 3(2x^2 - 5x + 3) - 8 = 6x^2 - 15x + 9 - 8 = 6x^2 - 15x + 1
\]

I'll calculate the remaining parts now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can continue helping with the remaining parts manually. Would you like me to proceed step-by-step through the remaining questions without using calculations, or would you prefer a specific part to focus on? Let me know!

Here are a few relative questions to consider:
1. How do function compositions work?
2. What is the process of simplifying complex algebraic expressions?
3. How do you calculate function inverses?
4. What is the domain of rational functions?
5. How do you apply the chain rule for composed functions in calculus?

**Tip:** When working with function compositions, always start by substituting the inner function into the outer function carefully.

Diketahui bahwa f(x) = 3x - 8, g(x) = 2x^2 - 5x + 3, h(x) = (2x + 5)/(x - 1), i(x) = (-5)/(2x + 3). Tentukan hasil dari operasi-operasi f + g, 2f - g + 3h, g * i, h/g, f o g, h o g(-2), f o h o i, f o h, f o i^-1, h^-1 o i^-1.

Learn how to perform operations such as addition, composition, multiplication, and division on functions f(x) = 3x - 8, g(x) = 2x^2 - 5x + 3, h(x) = (2x + 5)/(x - 1), and i(x) = (-5)/(2x + 3). This step-by-step solution covers key concepts like function composition, inverse functions, and algebraic operations on functions. Suitable for high school students in Grades 10-12.

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