Assume that the function  
f
  is a one-to-one function.

(a) If  
f
(
8
)
=
7
 , find  
f
−
1
(
7
)
 .
Your answer is

Since \( f \) is a one-to-one function, the inverse function \( f^{-1} \) undoes the action of \( f \). That is, if \( f(8) = 7 \), then the inverse \( f^{-1}(7) = 8 \).

Thus, the answer is:
\[
f^{-1}(7) = 8
\]

Would you like a detailed explanation on inverse functions, or do you have any other questions?

Here are 5 related questions you might find helpful:
1. What does it mean for a function to be one-to-one?
2. How do you verify if a function has an inverse?
3. What is the graphical interpretation of inverse functions?
4. Can a function have more than one inverse?
5. How do you find the inverse of a quadratic function?

**Tip:** A function is one-to-one if and only if every horizontal line intersects its graph at most once (this is called the Horizontal Line Test).

Assume that the function f is a one-to-one function. (a) If f(8) = 7, find f−1(7).

Learn how to find the inverse of a one-to-one function in this example where f(8) = 7. This problem covers key mathematical concepts like inverse functions and the one-to-one function property. Suitable for students in Grades 10-12.

Math Problem Statement

(a) If
f ( 8 )

Solution

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