Let's solve the problem step by step.

(a) Given:

• $f(6) = 8$
• We need to find $f^{-1}(8)$

From the definition of the inverse function, if $f(a) = b$, then $f^{-1}(b) = a$. In this case, since $f(6) = 8$, it follows that $f^{-1}(8) = 6$.

So, the answer for part (a) is:

$f^{-1}(8) = 6$

(b) Given:

• $f^{-1}(-4) = -2$
• We need to find $f(-2)$

Again, using the inverse function property, if $f^{-1}(b) = a$, then $f(a) = b$. Since $f^{-1}(-4) = -2$, we conclude that $f(-2) = -4$.

So, the answer for part (b) is:

$f(-2) = -4$

Would you like more details on inverse functions or have any questions?

Here are some related questions:

1. How can you verify that a function is one-to-one?
2. What is the graphical interpretation of a function and its inverse?
3. How do you find the inverse of a function algebraically?
4. What properties must a function satisfy to have an inverse?
5. How can you use inverse functions to solve equations?

Tip: Remember, a function is one-to-one if and only if no two different inputs map to the same output.