Math Problem Statement

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

(a) If
f ( 8 )

7 , find
f − 1 ( 7 ) . Your answer is

Solution

Since ff is a one-to-one function, the inverse function f1f^{-1} undoes the action of ff. That is, if f(8)=7f(8) = 7, then the inverse f1(7)=8f^{-1}(7) = 8.

Thus, the answer is: f1(7)=8f^{-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).

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Math Problem Analysis

Mathematical Concepts

Inverse Functions
One-to-One Functions

Formulas

f(f−1(x)) = x
f−1(f(x)) = x

Theorems

One-to-One Function Theorem
Inverse Function Property

Suitable Grade Level

Grades 10-12