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Let's work through the questions in the image step by step.

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### **1. Diberikan dua fungsi aljabar sebagai berikut:**
\( f(x) = \sqrt{2x + 5} \)  
\( g(x) = x^2 - 5x + 6 \)

#### (a) Tentukan hasil dari penjumlahan fungsi f dan g, yaitu \( (f + g)(x) \).

The sum of two functions is defined as:

\[
(f + g)(x) = f(x) + g(x)
\]

Thus:

\[
(f + g)(x) = \sqrt{2x + 5} + (x^2 - 5x + 6)
\]

This is the final expression for \( (f + g)(x) \).

#### (b) Temukan daerah asal dari fungsi \( (f + g)(x) \).

To find the domain (daerah asal), we need to consider the domain of both \( f(x) \) and \( g(x) \).

- For \( f(x) = \sqrt{2x + 5} \), the expression inside the square root must be non-negative:
  \[
  2x + 5 \geq 0 \implies x \geq -\frac{5}{2}
  \]
  So the domain of \( f(x) \) is \( x \geq -\frac{5}{2} \).

- For \( g(x) = x^2 - 5x + 6 \), the domain is all real numbers \( (-\infty, \infty) \).

The domain of \( (f + g)(x) \) is the intersection of both domains, which is \( x \geq -\frac{5}{2} \).

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### **2. Diketahui \( f(x) = x^2 + x - 12 \) dan \( g(x) = \frac{6x - 6}{5} \). Tentukan:**

#### (a) \( (f \circ g)(x) \)

Composition of functions \( (f \circ g)(x) \) is defined as \( f(g(x)) \). We substitute \( g(x) \) into \( f(x) \):

\[
f(g(x)) = f\left(\frac{6x - 6}{5}\right)
\]

Substitute \( g(x) \) into the expression for \( f(x) \):

\[
f\left(\frac{6x - 6}{5}\right) = \left(\frac{6x - 6}{5}\right)^2 + \left(\frac{6x - 6}{5}\right) - 12
\]

You can expand and simplify this expression to get the final result.

#### (b) \( (g \circ f)(x) \)

Composition of functions \( (g \circ f)(x) \) is defined as \( g(f(x)) \). We substitute \( f(x) \) into \( g(x) \):

\[
g(f(x)) = g(x^2 + x - 12)
\]

Substitute \( f(x) \) into the expression for \( g(x) \):

\[
g(x^2 + x - 12) = \frac{6(x^2 + x - 12) - 6}{5}
\]

Simplify the expression to get the final result.

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### **3. Berdasarkan soal nomor 2, jika diketahui \( h(x) = x^2 - 2x + 3 \), maka tentukan:**

#### (a) \( (h \circ f \circ g)(x) \)

This is the composition of three functions, i.e., \( h(f(g(x))) \). First, calculate \( f(g(x)) \) as in part 2a, and then substitute the result into \( h(x) \).

#### (b) \( (h \circ g \circ f)(x) \)

This is the composition of three functions, i.e., \( h(g(f(x))) \). First, calculate \( g(f(x)) \) as in part 2b, and then substitute the result into \( h(x) \).

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Would you like more detailed solutions for any part of these calculations?

### Related Questions:
1. How do you simplify function compositions like \( f(g(x)) \)?
2. What is the domain of a function involving square roots?
3. How can we find the range of a composed function?
4. Can we use graphs to understand function composition better?
5. How does composition of functions affect their domains?

### Tip:
Always check the domains of individual functions before composing them to ensure the input values are valid for all functions involved.

This problem involves the composition of algebraic functions and determining the domain of composite functions. Key concepts include adding and composing functions, understanding the domain of square root functions, and simplifying composite functions. Suitable for Grades 10-12 students.

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