Assume that the given function has an inverse function.

Given 

*f*(3) = 2, find *f* −1(2).

*f* −1(2)

 = 

To find \( f^{-1}(2) \), we need to understand that \( f^{-1}(x) \) is the inverse function of \( f(x) \). This means that if \( f(a) = b \), then \( f^{-1}(b) = a \).

Given that:
\[
f(3) = 2
\]
This implies that:
\[
f^{-1}(2) = 3
\]

Thus:
\[
f^{-1}(2) = 3
\]

Would you like more details or have any further questions?

Here are 5 related questions to consider:

1. What is the definition of an inverse function?
2. How do you determine if a function has an inverse?
3. If \( f^{-1}(b) = a \), what does \( f(a) \) equal?
4. How would you graphically interpret the inverse function of \( f(x) \)?
5. Can every function have an inverse? If not, why?

**Tip:** A function has an inverse only if it is one-to-one, meaning it passes both the horizontal and vertical line tests.

Assume that the given function has an inverse function. Given f(3) = 2, find f −1(2).

Learn how to find the inverse of a function with the example f(3) = 2. This solution explains the concept of inverse functions, including the key formula f(a) = b implies f^(-1)(b) = a. Suitable for students in Grades 9-12.

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