An inverse function is a function that "undoes" another function. If $f(x)$ takes $x$ to $y$, then the inverse function, denoted as $f^{-1}(x)$, takes $y$ back to $x$. In simpler terms, if you input a value into a function and then input the result into its inverse, you should get back your original value. To find the inverse, swap $x$ and $y$ in the original equation and then solve for $y$. Remember that not all functions have inverses; only one-to-one functions do.
This worksheet provides practice problems to help you master finding and working with inverse functions. Good luck! 👍
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Inverse Function | A. A function that maps each element of the range of a function back to its original value. |
| 2. One-to-One Function | B. A relation where each input has a unique output and vice versa. |
| 3. Domain | C. The set of all possible output values of a function. |
| 4. Range | D. The set of all possible input values of a function. |
| 5. Reflection | E. A transformation that flips a graph over a line, often $y=x$ for inverse functions. |
Answers: 1-A, 2-B, 3-D, 4-C, 5-E
To find the inverse of a function, you first ________ $x$ and $y$ in the equation. Then, you ________ for $y$. The inverse function is denoted as $f^{-1}(x)$. Not all functions have inverses; only ________ functions do. The graph of a function and its inverse are reflections of each other across the line ________.
Answers: swap, solve, one-to-one, $y=x$
Explain why it is important to check if a function is one-to-one before finding its inverse. What happens if you try to find the inverse of a function that is not one-to-one?
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