Let's go through the problems in your image step by step:

1. Jelaskan 3 jenis fungsi beserta contohnya!

(Explain 3 types of functions with examples!)

There are three main types of functions:

• Satu-satu (Injective) Function
  A function is injective if every element in the codomain is mapped by at most one element from the domain. No two different elements from the domain map to the same element in the codomain.
  Example: $f(x) = 2x + 3$ is injective because every value of $x$ maps to a unique $f(x)$.

• Pada (Surjective) Function
  A function is surjective if every element in the codomain has a pre-image in the domain. In other words, the entire codomain is "covered."
  Example: $g(x) = x^3$ is surjective when the codomain is all real numbers $\mathbb{R}$, because any real number can be the cube of some real number.

• Bijeksi (Bijective) Function
  A function is bijective if it is both injective and surjective. This means every element in the codomain is mapped by exactly one element in the domain, and vice versa.
  Example: $h(x) = 3x - 2$ is bijective when the domain and codomain are all real numbers, as it is both injective and surjective.

2. Berdasarkan ketiga diagram panah di atas, manakah yang merupakan relasi yang berupa fungsi dan yang bukan fungsi, jelaskan alasannya!

(Referring to the three arrow diagrams, which represent a function and which do not, explain your reasoning!)

• Diagram A:
  This is not a function because the element "a" in $X$ is mapped to both "m" and "n" in $Y$. A function requires that each element in the domain $X$ maps to exactly one element in $Y$.

• Diagram B:
  This is a function because each element in $X$ (a, b, c) maps to exactly one element in $Y$ (m, n, o).

• Diagram C:
  This is not a function because "q" in $X$ is mapped to both "x" and "y" in $Y$, violating the rule of functions where each element in $X$ must map to exactly one element in $Y$.

3. Diketahui $f(x) = x^2 + 2x + 3$ dan $g(x) = 3x + 2$. Tentukan $f(2) + g(5)$!

(Given $f(x) = x^2 + 2x + 3$ and $g(x) = 3x + 2$, find $f(2) + g(5)$!)

First, calculate each function value:

• $f(2) = 2^2 + 2(2) + 3 = 4 + 4 + 3 = 11$
• $g(5) = 3(5) + 2 = 15 + 2 = 17$

Now, add them together:

• $f(2) + g(5) = 11 + 17 = 28$

4. Diketahui $f(x) = 2x + 3$ dan $g(x) = x - 1$. Tentukan $f(x) + g(x)$ dan $f(x) - g(x)$!

(Given $f(x) = 2x + 3$ and $g(x) = x - 1$, find $f(x) + g(x)$ and $f(x) - g(x)$!)

• $f(x) + g(x) = (2x + 3) + (x - 1) = 3x + 2$
• $f(x) - g(x) = (2x + 3) - (x - 1) = 2x + 3 - x + 1 = x + 4$

Do you need any more detailed explanations on these answers?

Here are 5 related questions you can explore:

1. What are other examples of injective functions?
2. Can a function be injective but not surjective? Explain with an example.
3. How can you determine if a function is bijective?
4. What happens if you change the domain of $f(x) = x^2 + 2x + 3$? How does that affect its injectivity?
5. How do you compose two functions, and what does the composition tell you?

Tip: When verifying if a diagram represents a function, ensure that each element in the domain has only one corresponding element in the codomain.