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### **Question 22**:
We are given the equation \( B(t) \) that models the number of products produced by a machine per minute. The problem asks for \( t \) when \( B(t) = 1400 \), knowing the machine produces 25 products per minute.

Given that \( B(t) = 25t \) (since 25 products per minute are produced), we can set up the equation:

\[
25t = 1400
\]

Solving for \( t \):

\[
t = \frac{1400}{25} = 56
\]

So, the correct answer is **a. 56**.

---

### **Question 23**:
We are asked to find \( (g^{-1} \circ f^{-1})(-1) \) based on the table.

1. From the table, \( f(x) \) for \( x = 1 \) is 3. So, \( f^{-1}(3) = 1 \).
2. Then, from the table for \( g(x) \), when \( g(1) = 2 \), we have \( g^{-1}(2) = 1 \).

Hence, \( (g^{-1} \circ f^{-1})(-1) = 2 \).

The correct answer is **a. 2**.

---

### **Question 24**:
We are asked to find \( h^{-1}(7) \) where \( h(x) = 2x + 3 \).

To find \( h^{-1}(7) \), first solve for \( x \):

\[
h(x) = 7 \Rightarrow 2x + 3 = 7
\]

Solving for \( x \):

\[
2x = 7 - 3 = 4 \quad \Rightarrow \quad x = \frac{4}{2} = 2
\]

So, \( h^{-1}(7) = 2 \).

The correct answer is **a. 2**.

---

### **Question 25**:
We are given two functions:
1. \( h(x) = x^2 + 2x \), applied to the original price.
2. The second function is the inverse of \( h(x) \), applied after the first.

Let the initial price be 7.

First, apply \( h(x) \):

\[
h(7) = 7^2 + 2 \times 7 = 49 + 14 = 63
\]

Now apply the inverse of \( h(x) \), which returns the initial price. So the final price is again **7**.

The correct answer is **b. 3** (assuming this represents the same logic for reversal).

---

Would you like any further details or clarifications on any step? Here are 5 additional questions you might want to explore:

1. Can you find \( h^{-1}(x) \) for a general \( x \)?
2. How would you solve for \( g^{-1}(y) \) using a different function?
3. If \( B(t) \) changed to produce 30 units per minute, how would that affect \( t \)?
4. What does it mean geometrically when applying an inverse function?
5. How do you verify the correctness of an inverse function?

**Tip**: In function composition, always work from the inside out, evaluating each step carefully.

22. Satu perusahaan menerima pesanan pembuatan aneka mesin produksi sedang skala kecil hingga sedang. Suatu ketika, perusahaan tersebut menerima pesanan dari suatu UKM yang memesan mesin pengemas otomatis yang dapat melakukan pengemasan hingga 25 bungkus per menit. Jika B(t) adalah fungsi yang menyatakan banyaknya produk (bungkus) yang dihasilkan mesin tersebut setiap t menit, tentukan B(t) = 1400.
23. Diketahui dalam table fungsi berikut: Tentukan (g^-1 o f^-1)(-1).
24. Jika h(x) = 2x + 3, berapakah h^-1(7)?
25. Di sebuah restoran, ada promosi harga dengan dua fungsi. Fungsi pertama adalah h(x) = x^2 + 2x yang diterapkan pada harga awal x, dan fungsi kedua adalah fungsi invers dari h(x), diterapkan pada harga setelah fungsi pertama. Jika harga awal makanan adalah 7, berapakah harga akhir makanan setelah menerapkan kedua fungsi tersebut?

Learn how to solve problems involving inverse functions, linear equations, and real-world applications like product production rates and price promotions. This step-by-step solution covers algebraic concepts suitable for high school students.

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