Math Problem Statement
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πβ1(β4)=
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πβ1(β3)=
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πβ1(0)=
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πβ1(2)=
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πβ1(4)=
Solution
Let's analyze the image, which appears to be a graph of a function . To answer the questions regarding , or the inverse function, we need to find the -values for specific -values (since if and only if ).
Hereβs the breakdown based on the graph:
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: This is the -value where . From the graph, it appears that the point where corresponds to . So, .
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: The -value where corresponds to from the graph. So, .
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: The point where corresponds to . Thus, .
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: For , there doesnβt seem to be a corresponding point on the visible part of the graph, so it's likely undefined within this range.
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: For , similar to , thereβs no corresponding -value on the visible graph.
To summarize:
- is undefined
- is undefined
Would you like further details or clarification?
Here are five questions related to this graph and inverse functions:
- How is the domain of determined from the original function?
- What does it mean for the function if is undefined for certain values?
- How would the functionβs behavior change if the graph extended beyond the current range?
- What properties must the function have to ensure that exists?
- How would you calculate the inverse function algebraically if given a formula for ?
Tip: When looking at graphs of functions and their inverses, reflect the graph over the line to visualize the inverse relationship more easily!
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Math Problem Analysis
Mathematical Concepts
Inverse functions
Graph interpretation
Formulas
f^{-1}(y) = x if and only if f(x) = y
Theorems
Inverse function theorem
Suitable Grade Level
Grades 9-12