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The question asks for the inverse functions of the given functions. Let's solve them one by one:

1. **f(x) = 3x - 7**
   - To find the inverse, swap \(x\) and \(y\) in the equation:
     \[
     y = 3x - 7
     \]
     Swap \(x\) and \(y\):
     \[
     x = 3y - 7
     \]
     Solve for \(y\):
     \[
     x + 7 = 3y \implies y = \frac{x + 7}{3}
     \]
     Therefore, the inverse function is:
     \[
     f^{-1}(x) = \frac{x + 7}{3}
     \]

2. **g(x) = 9 - 2x**
   - Start by swapping \(x\) and \(y\):
     \[
     y = 9 - 2x
     \]
     Swap \(x\) and \(y\):
     \[
     x = 9 - 2y
     \]
     Solve for \(y\):
     \[
     2y = 9 - x \implies y = \frac{9 - x}{2}
     \]
     Therefore, the inverse function is:
     \[
     g^{-1}(x) = \frac{9 - x}{2}
     \]

3. **h(x) = \frac{1}{4}x + 5**
   - Swap \(x\) and \(y\):
     \[
     y = \frac{1}{4}x + 5
     \]
     Swap \(x\) and \(y\):
     \[
     x = \frac{1}{4}y + 5
     \]
     Solve for \(y\):
     \[
     x - 5 = \frac{1}{4}y \implies y = 4(x - 5)
     \]
     Therefore, the inverse function is:
     \[
     h^{-1}(x) = 4(x - 5)
     \]

4. **k(x) = 2 - \frac{1}{5}x**
   - Swap \(x\) and \(y\):
     \[
     y = 2 - \frac{1}{5}x
     \]
     Swap \(x\) and \(y\):
     \[
     x = 2 - \frac{1}{5}y
     \]
     Solve for \(y\):
     \[
     \frac{1}{5}y = 2 - x \implies y = 5(2 - x)
     \]
     Therefore, the inverse function is:
     \[
     k^{-1}(x) = 5(2 - x)
     \]

Do you want more details, or do you have any questions?

Here are five related questions for you to consider:
1. How can you verify if a function is one-to-one before finding its inverse?
2. What is the graphical relationship between a function and its inverse?
3. Can all functions have an inverse? If not, why?
4. How can you use the horizontal line test to check if a function has an inverse?
5. What happens to the domain and range of a function when you find its inverse?

**Tip:** To check if your inverse function is correct, compose the original and inverse functions. The result should be \(x\).

Find the inverse of the following functions: f(x) = 3x - 7, g(x) = 9 - 2x, h(x) = (1/4)x + 5, k(x) = 2 - (1/5)x

Learn how to find the inverse of linear functions with examples such as f(x) = 3x - 7, g(x) = 9 - 2x, h(x) = (1/4)x + 5, and k(x) = 2 - (1/5)x. This step-by-step guide helps students in Grades 10-12 understand the process of swapping variables and solving for the inverse function.

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