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Let's go through each function step by step to find their inverses.

1. **\( f(x) = 3x - 5 \)**:
   - To find the inverse, first replace \( f(x) \) with \( y \):  
     \( y = 3x - 5 \)
   - Switch \( x \) and \( y \):  
     \( x = 3y - 5 \)
   - Solve for \( y \):  
     \( y = \frac{x + 5}{3} \)
   - So, the inverse is \( f^{-1}(x) = \frac{x + 5}{3} \).

2. **\( f(x) = 5x + 7 \)**:
   - Replace \( f(x) \) with \( y \):  
     \( y = 5x + 7 \)
   - Switch \( x \) and \( y \):  
     \( x = 5y + 7 \)
   - Solve for \( y \):  
     \( y = \frac{x - 7}{5} \)
   - So, the inverse is \( f^{-1}(x) = \frac{x - 7}{5} \).

3. **\( f(x) = \frac{x + 5}{2x - 6} \)**:
   - Replace \( f(x) \) with \( y \):  
     \( y = \frac{x + 5}{2x - 6} \)
   - Switch \( x \) and \( y \):  
     \( x = \frac{y + 5}{2y - 6} \)
   - Solve for \( y \) by cross-multiplying:  
     \( x(2y - 6) = y + 5 \)  
     \( 2xy - 6x = y + 5 \)
   - Group the terms with \( y \):  
     \( 2xy - y = 6x + 5 \)  
     \( y(2x - 1) = 6x + 5 \)
   - Solve for \( y \):  
     \( y = \frac{6x + 5}{2x - 1} \)
   - So, the inverse is \( f^{-1}(x) = \frac{6x + 5}{2x - 1} \).

4. **\( f(x) = \frac{2x + 1}{8x - 5} \)**:
   - Replace \( f(x) \) with \( y \):  
     \( y = \frac{2x + 1}{8x - 5} \)
   - Switch \( x \) and \( y \):  
     \( x = \frac{2y + 1}{8y - 5} \)
   - Solve for \( y \) by cross-multiplying:  
     \( x(8y - 5) = 2y + 1 \)  
     \( 8xy - 5x = 2y + 1 \)
   - Group the terms with \( y \):  
     \( 8xy - 2y = 5x + 1 \)  
     \( y(8x - 2) = 5x + 1 \)
   - Solve for \( y \):  
     \( y = \frac{5x + 1}{8x - 2} \)
   - So, the inverse is \( f^{-1}(x) = \frac{5x + 1}{8x - 2} \).

5. **\( f(x) = \frac{x + 1}{7 - 6x} \)**:
   - Replace \( f(x) \) with \( y \):  
     \( y = \frac{x + 1}{7 - 6x} \)
   - Switch \( x \) and \( y \):  
     \( x = \frac{y + 1}{7 - 6y} \)
   - Solve for \( y \) by cross-multiplying:  
     \( x(7 - 6y) = y + 1 \)  
     \( 7x - 6xy = y + 1 \)
   - Group the terms with \( y \):  
     \( 7x - 1 = y + 6xy \)  
     \( 7x - 1 = y(1 + 6x) \)
   - Solve for \( y \):  
     \( y = \frac{7x - 1}{1 + 6x} \)
   - So, the inverse is \( f^{-1}(x) = \frac{7x - 1}{1 + 6x} \).

Would you like more details on any step? Here are some related questions:

1. What is the general process for finding the inverse of a function?
2. How can we verify that two functions are inverses of each other?
3. Why is switching \( x \) and \( y \) a key step in finding the inverse?
4. What kind of functions do not have inverses, and why?
5. How do we deal with more complex functions, such as those involving higher-degree polynomials, when finding inverses?

**Tip**: Always check if a function is one-to-one before finding its inverse, as non-invertible functions cannot have proper inverses.

Tentukan fungsi invers berikut: 1. f(x) = 3x - 5, 2. f(x) = 5x + 7, 3. f(x) = (x + 5)/(2x - 6), 4. f(x) = (2x + 1)/(8x - 5), 5. f(x) = (x + 1)/(7 - 6x).

This problem involves finding the inverse functions of five different functions, including both linear and rational functions. Suitable for high school students, the problem covers key algebraic concepts such as switching variables and solving equations.

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