https://file.aiquickdraw.com/mathbot/file/1727790211327laibrker.jpg

The problem in the image is asking to calculate how many products must be sold to achieve a profit of Rp 100,000 using an inverse function. The function provided is:

\[
f(x) = 4x + 8
\]

where:
- \( x \) is the number of products sold, and
- \( f(x) \) is the profit in thousands of Rupiah.

To solve this problem using the inverse function, we follow these steps:

### Step 1: Set up the function equation
The goal is to find how many products must be sold to earn a profit of Rp 100,000. Since the profit function \( f(x) \) is in thousands of Rupiah, the target profit is:

\[
f(x) = 100
\]

Thus, we have the equation:

\[
100 = 4x + 8
\]

### Step 2: Solve for \( x \)
To isolate \( x \), subtract 8 from both sides:

\[
100 - 8 = 4x
\]

\[
92 = 4x
\]

Now, divide both sides by 4:

\[
x = \frac{92}{4} = 23
\]

### Conclusion:
The number of products that must be sold to achieve a profit of Rp 100,000 is **23 products**.

Would you like more details on the inverse function, or do you have any questions?

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Here are 5 related questions:
1. How would the answer change if the profit target was Rp 150,000?
2. How can we interpret the function \( f(x) = 4x + 8 \) graphically?
3. What does the constant 8 represent in the equation \( f(x) = 4x + 8 \)?
4. How do you derive the inverse of a linear function like \( f(x) = 4x + 8 \)?
5. If the profit per product increases, how would that affect the required number of products sold?

**Tip**: In general, for any linear function \( f(x) = ax + b \), you can always find \( x \) by solving \( f(x) = y \) through simple algebra.

Seorang pengusaha memiliki rumus untuk menghitung keuntungan harian dari produknya, yaitu f(x) = 4x + 8, dimana x adalah jumlah produk yang terjual, dan f(x) adalah keuntungan dalam ribu rupiah. Suatu hari pengusaha tersebut ingin mengetahui berapa banyak produk yang harus dijual jika ingin memperoleh keuntungan sebesar Rp 100.000,-. Tentukan jumlah produk yang harus dijual dengan menggunakan fungsi invers!

Learn how to use an inverse function to determine the number of products that must be sold to achieve a profit of Rp 100,000. The solution uses the linear equation f(x) = 4x + 8 and involves algebraic techniques. Suitable for Grades 10-12 students.

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