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The given function is \( h(x) = 8x \), and we are asked to find an expression for the inverse function \( h^{-1}(x) \).

To find the inverse of a function, we follow these steps:

1. Replace \( h(x) \) with \( y \), so we have:
   \[
   y = 8x
   \]

2. Swap \( x \) and \( y \) to prepare for solving for \( y \):
   \[
   x = 8y
   \]

3. Solve for \( y \) in terms of \( x \):
   \[
   y = \frac{x}{8}
   \]

4. Therefore, the inverse function is:
   \[
   h^{-1}(x) = \frac{x}{8}
   \]

This is the expression for the inverse of \( h(x) = 8x \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the general process to find the inverse of a function?
2. Can every function have an inverse? If not, why?
3. How can we verify that two functions are inverses of each other?
4. What are the domain and range of the inverse function \( h^{-1}(x) \)?
5. How would the process differ if the original function were nonlinear?

**Tip**: To check if you've found the correct inverse, compose the original function with its inverse (i.e., \( h(h^{-1}(x)) \)) and confirm if the result is \( x \).

Work out an expression for h^{-1}(x) given that h(x) = 8x.

Learn how to find the inverse function h^{-1}(x) for the linear function h(x) = 8x. This problem involves understanding basic algebraic manipulations and the concept of inverse functions, suitable for Grades 9-11.

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