To rewrite the equation, follow these steps systematically:

1. Replace $f(x)$ with $y$:

Suppose the original function is $f(x) = g(x)$ (replace $g(x)$ with the specific function given in your problem). Rewrite it as: $y = g(x)$

2. Interchange $x$ and $y$:

Swap $x$ and $y$ in the equation: $x = g(y)$

3. Solve the new equation for $y$:

Rearrange the equation to express $y$ in terms of $x$. This step may require algebraic manipulation, logarithms, square roots, or other methods depending on $g(y)$.

4. Check if the equation has a unique solution for $y$:

Determine if $y$ is uniquely defined for all $x$. This means checking that the original function is one-to-one, often by verifying that its derivative does not change sign (monotonicity) or using other properties.

5. Replace $y$ with $f^{-1}(x)$:

Once $y$ is expressed in terms of $x$, denote it as the inverse function: $f^{-1}(x) = h(x)$ (where $h(x)$ is the result of solving for $y$).

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Let me know if you want me to work through an explicit example or if you'd like to clarify the original function!

Here are five related questions for you to consider:

1. What is the specific function you're working with?
2. How do you determine if a function is one-to-one?
3. What are the algebraic challenges in solving for $y$ in your function?
4. Can all functions have inverses? Why or why not?
5. What is the graphical interpretation of finding an inverse function?

Tip: Always check the domain and range of the original function and its inverse to ensure they align correctly!