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Let's solve the given problems one by one:

### Problem 3:
**Diketahui g(x) = 2x + 3 dan f(x) = x² − 4x + 6, maka (f o g)(x) adalah…**

We need to find the composition \( (f \circ g)(x) \), which means \( f(g(x)) \). This is done by substituting \( g(x) \) into the function \( f(x) \).

Given:
- \( g(x) = 2x + 3 \)
- \( f(x) = x^2 - 4x + 6 \)

Now, substitute \( g(x) = 2x + 3 \) into \( f(x) \):

\[
f(g(x)) = f(2x + 3) = (2x + 3)^2 - 4(2x + 3) + 6
\]

First, calculate \( (2x + 3)^2 \):
\[
(2x + 3)^2 = 4x^2 + 12x + 9
\]

Next, calculate \( -4(2x + 3) \):
\[
-4(2x + 3) = -8x - 12
\]

Now, put everything together:
\[
f(g(x)) = 4x^2 + 12x + 9 - 8x - 12 + 6
\]
\[
f(g(x)) = 4x^2 + 4x + 3
\]

Thus, the correct answer is **e. 4x² + 4x + 3**.

---

### Problem 4:
**Jika f(x) = x² + 2x dan g(x) = x − 1, maka (f o g)(10) adalah…**

We need to find \( (f \circ g)(10) = f(g(10)) \).

First, find \( g(10) \):
\[
g(10) = 10 - 1 = 9
\]

Next, substitute \( g(10) = 9 \) into \( f(x) \):
\[
f(9) = 9^2 + 2(9) = 81 + 18 = 99
\]

Thus, the correct answer is **e. 99**.

---

### Problem 5:
**Diketahui fungsi f: ℝ → ℝ dan g: ℝ → ℝ, di mana f(x) = 2x + 1 dan g(x) = x² − 1. Maka fungsi komposisi (g o f)(x) adalah…**

We need to find \( (g \circ f)(x) = g(f(x)) \).

Given:
- \( f(x) = 2x + 1 \)
- \( g(x) = x^2 - 1 \)

Substitute \( f(x) = 2x + 1 \) into \( g(x) \):

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

First, calculate \( (2x + 1)^2 \):
\[
(2x + 1)^2 = 4x^2 + 4x + 1
\]

Now, subtract 1:
\[
g(f(x)) = 4x^2 + 4x + 1 - 1 = 4x^2 + 4x
\]

Thus, the correct answer is **b. 4x² + 4x**.

---

Would you like further explanations or have any questions on these problems?

Here are 5 additional questions that extend the concepts:
1. How does function composition differ from addition or multiplication of functions?
2. Can the order of function composition \( f \circ g \) and \( g \circ f \) change the result?
3. What happens when one of the functions in a composition is a constant function?
4. How would you compute the composition of more than two functions, say \( h \circ g \circ f(x) \)?
5. How can you interpret function composition in real-world applications?

### Tip:
When performing function composition, carefully substitute the entire expression of one function into the other, ensuring each step is computed correctly.

Diketahui g(x) = 2x + 3 dan f(x) = x² − 4x + 6, maka (f o g)(x) adalah; Jika f(x) = x² + 2x dan g(x) = x − 1, maka (f o g)(10) adalah; Diketahui fungsi f: ℝ → ℝ dan g: ℝ → ℝ, di mana f(x) = 2x + 1 dan g(x) = x² − 1. Maka fungsi komposisi (g o f)(x) adalah

Learn how to solve function composition problems involving quadratic functions. This problem set covers key concepts such as algebraic function composition, expanding quadratic expressions, and step-by-step solutions. Suitable for Grades 10-12.

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