Math Problem Statement
Use the table below to fill in the missing values:
1. f(2) = ?
2. If f(x) = 9, then x = ?
3. f⁻¹(6) = ?
4. f⁻¹(3) = ?
Solution
The image displays a table and several questions related to a function . The table has two columns: and . I'll extract the relevant data from the table and solve the questions below it.
Table:
\hline x & f(x) \\ \hline 0 & 8 \\ 1 & 5 \\ 2 & 6 \\ 3 & 7 \\ 4 & 0 \\ 5 & 2 \\ 6 & 3 \\ 7 & 4 \\ \hline \end{array}$$ ### Questions: 1. $$f(2) =$$ ? 2. If $$f(x) = 9$$, then $$x =$$ ? 3. $$f^{-1}(6) =$$ ? 4. $$f^{-1}(3) =$$ ? I'll now calculate the answers to each of these questions using the data from the table.Here are the answers based on the table provided: 1. $$f(2) = 6$$ 2. If $$f(x) = 9$$, then $$x =$$ No solution (there is no $$x$$ for which $$f(x) = 9$$) 3. $$f^{-1}(6) = 2$$ (this means $$f(2) = 6$$) 4. $$f^{-1}(3) = 6$$ (this means $$f(6) = 3$$) Would you like further explanation on any of these points, or do you have more questions? ### Related Questions: 1. What does the inverse function $$f^{-1}(x)$$ represent in general? 2. How do we interpret the table in terms of finding the inverse function? 3. What happens if we encounter a function that is not one-to-one? Can it have an inverse? 4. Can you determine a function that could produce $$f(x) = 9$$? 5. How do we graphically represent $$f(x)$$ and its inverse? **Tip:** Remember, an inverse function exists only when the original function is one-to-one (each $$y$$ value corresponds to exactly one $$x$$ value).Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Functions
Inverse Functions
Reading from a Table
Formulas
f(x) represents the function value for a given x
f⁻¹(y) represents the x value for a given function output y
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 8-10