Math Problem Statement
how to solve d
How to solve (g(2))^-1 using the given table of functions f and g.
Solution
To solve part (d), , we need to determine the value of from the table, then find the inverse value corresponding to that result for .
Step-by-Step Solution:
-
Find :
Look up the value of when in the table. From the table,
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Find the inverse :
Now, we need to find the value of such that . From the table,
Therefore,
Conclusion:
The value of is .
If you have any further questions or want more details, feel free to ask!
Related Questions:
- What is the general method for finding inverses of functions?
- How do you compute compositions of functions using tables?
- What are some examples of functions where the inverse is not well-defined?
- Can you explain how to determine whether a function is invertible from a table?
- What are some practical applications of inverse functions in real life?
Tip:
Always check the domain and range of a function to ensure the inverse is valid and within the correct values.
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Math Problem Analysis
Mathematical Concepts
Functions
Function Inverses
Composition of Functions
Formulas
g(x) = y, g^{-1}(y) = x
Theorems
Inverse function theorem
Properties of invertible functions
Suitable Grade Level
Grades 9-12