https://file.aiquickdraw.com/mathbot/file/1728793654321w2fx730c.jpg

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:

\[
f^{-1}(8) = 6
\]

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**(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?

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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.

Assume that the function f is a one-to-one function. (a) If f(6) = 8, find f^{-1}(8). (b) If f^{-1}(-4) = -2, find f(-2).

Solve an inverse function problem where f(6) = 8 and f^{-1}(-4) = -2. Learn how to use the properties of inverse functions to find f^{-1}(8) and f(-2) with a detailed solution. Ideal for students in Grades 9-12.

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