Math Problem Statement
Using the graph, determine the value of f^{-1}(3).
Solution
To solve for using the graph, we need to find the value of such that . In other words, find the -coordinate where the function outputs 3.
Steps to Determine :
- Identify the point on the graph where .
- Find the corresponding -value for that -coordinate.
From the graph:
- When , the corresponding -value is 5.
Therefore:
Final Answer:
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Related Questions:
- What is the definition of an inverse function?
- How do you verify that two functions are inverses of each other?
- What is the general process for finding algebraically?
- How can you check if a function is one-to-one (invertible) using the graph?
- How do you determine when given a table of values?
Tip:
The graph of a function and its inverse are symmetric about the line . This symmetry can help verify inverse relationships visually.
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Graph Analysis
Linear Functions
Formulas
Inverse function property: f^{-1}(y) = x where f(x) = y
Theorems
The graph of a function and its inverse are symmetric about the line y = x.
Suitable Grade Level
Grade 10-11