The whiteboard contains a set of math problems written in Indonesian. Here is a translation and breakdown of the contents:

1) Jika $f \left( \frac{1}{2}x \right) = \frac{x^2}{x-1}$

Tentukan $f(x)$ (Determine $f(x)$).

2) Jika $f(x) = \frac{1}{x}$ dan $g(x) = \frac{x^2 - 1}{x + 2}$, maka nilai $(fog)(3)$ adalah?

(If $f(x) = \frac{1}{x}$ and $g(x) = \frac{x^2 - 1}{x + 2}$, find the value of $(fog)(3)$).

3) Jika $h(x) = \frac{x + 5}{x}$ dan $f(x) = g(x)$, maka $h(x) \cdot g(x)$ adalah...

(If $h(x) = \frac{x + 5}{x}$ and $f(x) = g(x)$, then $h(x) \cdot g(x)$ is...).

4) Diketahui $f(x) = \frac{x + 7}{x}$ dan $g(x) = \frac{x}{x + 2}$, serta $h(x) = \frac{x + 1}{x}$, maka $(fog)h(x)$ adalah...

(Given $f(x) = \frac{x + 7}{x}$, $g(x) = \frac{x}{x + 2}$, and $h(x) = \frac{x + 1}{x}$, find $(fog)h(x)$).

5) Jika $(fog)(x) = 6x - 3$ dan $f(x) = 2x + 5$, maka tentukan $g(x)$ (If $(fog)(x) = 6x - 3$ and $f(x) = 2x + 5$, find $g(x)$).

6) Jika $f(g(f(x))) = 2x^3 - 3$ dan $g(x) = 2x + 1$, tentukan $ff(x)$ (If $f(g(f(x))) = 2x^3 - 3$ and $g(x) = 2x + 1$, find $ff(x)$).

The rest of the board seems to include some explanations and context for these problems, along with some word problems related to economic functions, but it is quite faint.

Would you like help solving any specific part of this? Let me know if you'd like further clarification on the problems.

Here are 5 relative questions you might explore further:

1. How can we find $f(x)$ from $f\left(\frac{1}{2}x\right)$?
2. What is the process of composing two functions, such as $(fog)(x)$?
3. How does the function composition behave when we have multiple layers, such as in $f(g(f(x)))$?
4. What steps are involved in finding $g(x)$ when $f(x)$ and $(fog)(x)$ are given?
5. How does functional composition change if the functions have fractional expressions?

Tip: When composing functions, always substitute the output of the inner function into the outer function carefully.