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The image you've provided contains mathematical problems regarding the composition of functions. Let me break down each part of the image and solve the problems step by step.

### Part A
#### a. Diberikan fungsi \( f: R \to R \) dan \( g: R \to R \) yang didefinisikan oleh \( f(x) = 2x^2 + 1 \) dan \( g(x) = -2x + 5 \).

1. Tentukan \( (g \circ f)(x) \).

This is asking for the composition of \( g \) and \( f \), which means we need to substitute \( f(x) \) into \( g(x) \):

\[
(g \circ f)(x) = g(f(x)) = g(2x^2 + 1)
\]
Substitute \( x \) in \( g(x) = -2x + 5 \) with \( 2x^2 + 1 \):
\[
g(2x^2 + 1) = -2(2x^2 + 1) + 5 = -4x^2 - 2 + 5 = -4x^2 + 3
\]
Thus, \( (g \circ f)(x) = -4x^2 + 3 \).

2. Tentukan \( (f \circ g)(x) \).

Similarly, we now need to substitute \( g(x) = -2x + 5 \) into \( f(x) \):
\[
(f \circ g)(x) = f(g(x)) = f(-2x + 5)
\]
Substitute \( -2x + 5 \) into \( f(x) = 2x^2 + 1 \):
\[
f(-2x + 5) = 2(-2x + 5)^2 + 1
\]
First, expand \( (-2x + 5)^2 \):
\[
(-2x + 5)^2 = 4x^2 - 20x + 25
\]
Now substitute into \( f \):
\[
f(-2x + 5) = 2(4x^2 - 20x + 25) + 1 = 8x^2 - 40x + 50 + 1 = 8x^2 - 40x + 51
\]
Thus, \( (f \circ g)(x) = 8x^2 - 40x + 51 \).

---

### Part B
#### b. Diberikan fungsi \( f: R \to R \), \( g: R \to R \), dan \( h: R \to R \) dengan definisi \( f(x) = 2x \), \( g(x) = x + 2 \), dan \( h(x) = x^2 + 1 \).

1. Tentukan \( (f \circ g \circ h)(x) \).

We need to perform the composition \( (f \circ g \circ h)(x) = f(g(h(x))) \).

Start by finding \( h(x) \):
\[
h(x) = x^2 + 1
\]

Now substitute \( h(x) \) into \( g(x) = x + 2 \):
\[
g(h(x)) = g(x^2 + 1) = (x^2 + 1) + 2 = x^2 + 3
\]

Finally, substitute \( g(h(x)) \) into \( f(x) = 2x \):
\[
f(g(h(x))) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6
\]

Thus, \( (f \circ g \circ h)(x) = 2x^2 + 6 \).

---

### Part C
#### c. Diberikan fungsi \( f(x) = 2x^2 + 5 \) dan \( g(x) = 3x + 1 \).

1. Tentukan \( (f \circ g)(x) \).

We need to substitute \( g(x) = 3x + 1 \) into \( f(x) \):
\[
(f \circ g)(x) = f(g(x)) = f(3x + 1)
\]
Substitute \( 3x + 1 \) into \( f(x) = 2x^2 + 5 \):
\[
f(3x + 1) = 2(3x + 1)^2 + 5
\]
First, expand \( (3x + 1)^2 \):
\[
(3x + 1)^2 = 9x^2 + 6x + 1
\]
Now substitute into \( f \):
\[
f(3x + 1) = 2(9x^2 + 6x + 1) + 5 = 18x^2 + 12x + 2 + 5 = 18x^2 + 12x + 7
\]

Thus, \( (f \circ g)(x) = 18x^2 + 12x + 7 \).

---

The final question asks:
"Tentukan komposisi dari hasil di komposisi kedua apakah komposisi berurutan pada fungsi berbeda memberikan hasil yang berbeda?"

Yes, the order of composition generally affects the result. For instance, \( (f \circ g)(x) \) and \( (g \circ f)(x) \) often give different outcomes because the operations are applied in a different sequence.

---

Would you like more details on any step or have any specific questions?

### 5 Related Questions:
1. What are the general properties of function composition?
2. How does function composition relate to the identity function?
3. Can function compositions be undone? What is the role of inverse functions here?
4. What happens when you compose functions involving logarithms or trigonometric functions?
5. How is function composition used in real-world scenarios, such as in computer science?

### Tip:
When solving compositions, always handle the innermost function first, working your way outwards step by step.

Find the composition of functions for the given mathematical functions.

Explore the detailed solutions for finding the composition of functions, including (g ∘ f)(x) and (f ∘ g)(x). The problems involve key concepts in algebra and function composition. Suitable for high school students.

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