Math Problem Statement

The graph of f ^ - 1 is obtained by reflecting the graph of f about the y-axis true or false

Solution

False.

The graph of f1f^{-1} (the inverse of ff) is obtained by reflecting the graph of ff across the line y=xy = x, not the y-axis.

Would you like further details or have any other questions?

Here are 5 related questions to expand your understanding:

  1. How is the graph of a function reflected across the y-axis?
  2. What conditions must a function meet to have an inverse?
  3. How does the derivative of a function relate to the derivative of its inverse?
  4. How do you find the inverse of a function algebraically?
  5. What does it mean when a function is not invertible?

Tip: For a function to have an inverse, it must be one-to-one, meaning it passes the horizontal line test.

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Math Problem Analysis

Mathematical Concepts

Functions
Inverse Functions
Graph Reflections

Formulas

Reflection across y = x for inverse functions

Theorems

Inverse Function Theorem
Horizontal Line Test

Suitable Grade Level

Grades 10-12