Math Problem Statement

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

Solution

If f1(7)=8f^{-1}(-7) = -8, it means that f(8)=7f(-8) = -7. This is because the inverse function, f1(x)f^{-1}(x), undoes the action of the original function f(x)f(x). So:

f1(7)=8    f(8)=7f^{-1}(-7) = -8 \implies f(-8) = -7

Thus, f(8)=7f(-8) = -7.

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

Here are 5 related questions:

  1. What is the general process of finding an inverse function?
  2. How do you verify that two functions are inverses of each other?
  3. How do you solve for f(x)f(x) when given a point on the graph of f1(x)f^{-1}(x)?
  4. What are the properties of inverse functions?
  5. Can a function have more than one inverse?

Tip: The graph of a function and its inverse are reflections across the line y=xy = x.

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Math Problem Analysis

Mathematical Concepts

Inverse Functions
Function Composition

Formulas

f(f^{-1}(x)) = x and f^{-1}(f(x)) = x

Theorems

Inverse Function Theorem

Suitable Grade Level

Grades 9-12