Math Problem Statement
A table of values for f(x) is given. Complete the table for f^{-1}(x) for each corresponding set of values from f(x).
Solution
The table in the image gives the function values for specific -values, and you are asked to find the corresponding values of the inverse function .
Here is the given data for :
x & f(x) \\ \hline -3 & 5 \\ -2 & 4 \\ -1 & 1 \\ 0 & -4 \\ 1 & 11 \\ \end{array}$$ To find $$f^{-1}(x)$$, recall that for a function and its inverse, $$f^{-1}(f(x)) = x$$. This means that if $$f(a) = b$$, then $$f^{-1}(b) = a$$. Thus, for the inverse function table: $$\begin{array}{c|c} f(x) & f^{-1}(x) \\ \hline 5 & -3 \\ 4 & -2 \\ 1 & -1 \\ -4 & 0 \\ 11 & 1 \\ \end{array}$$ The values for $$f^{-1}(x)$$ can be filled in as: - $$f^{-1}(5) = -3$$ - $$f^{-1}(4) = -2$$ - $$f^{-1}(1) = -1$$ - $$f^{-1}(-4) = 0$$ - $$f^{-1}(11) = 1$$ Let me know if you need further clarifications! Here are 5 related questions: 1. How do we determine if a function has an inverse? 2. What conditions must be satisfied for a function to be one-to-one? 3. Can all functions have an inverse function? Why or why not? 4. How is the graph of $$f^{-1}(x)$$ related to the graph of $$f(x)$$? 5. How do you algebraically find the inverse of a function? **Tip:** The graph of a function and its inverse are reflections of each other across the line $$y = x$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Functions
Inverse Functions
Algebra
Formulas
f^{-1}(f(x)) = x
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 9-12