Math Problem Statement
Use the given graph of y = f(x) to evaluate the following: (a) f(-3), (b) f(2), (c) f^(-1)(1), (d) f^(-1)(-3).
Solution
The image provided shows a question based on the graph of a function . To evaluate the answers, we can read the function values from the graph.
The points provided on the graph are:
- (this is the x-value where )
- (this is the x-value where )
Let's break it down:
- (a) : From the graph, when , .
- (b) : From the graph, when , .
- (c) : The inverse asks for the x-value when , which is .
- (d) : The inverse asks for the x-value when , which is .
Now, you can proceed to fill in the answers for each part of the question:
- (a)
- (b)
- (c)
- (d)
Would you like more details on inverse functions or any other concept?
Here are some related questions:
- What is the graphical interpretation of an inverse function?
- How can you verify if a function is one-to-one and thus invertible?
- Can a function have an inverse if it is not one-to-one?
- How does the horizontal line test help in determining invertibility?
- What are some examples of real-world applications of inverse functions?
Tip: Inverse functions swap the input and output values of the original function, so visually, they reflect across the line .
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Math Problem Analysis
Mathematical Concepts
Functions
Inverse Functions
Graph Interpretation
Formulas
-
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 9-12