To find $f^{-1}(-6)$, we need to determine the value of $x$ such that $f(x) = -6$.

Since the function $f(x)$ is invertible, there exists a unique value $x$ for which $f(x) = -6$.

The inverse function $f^{-1}(x)$ essentially reverses the operation of $f(x)$. So, $f^{-1}(-6) = x$ if $f(x) = -6$.

To find the exact value of $f^{-1}(-6)$, I need more information about the function $f(x)$. Can you provide the explicit form of $f(x)$?

Would you like to go into further details on this, or have any additional questions? Here are five related questions to consider:

1. What steps are involved in finding the inverse of a function?
2. How do you verify if a function is invertible?
3. What are the general conditions for a function to have an inverse?
4. How do you graphically interpret the inverse of a function?
5. How do you apply the inverse function in real-world problems?

Tip: When working with inverse functions, always check the domain and range of the original function to ensure that the inverse function is well-defined.