What is the "pre-image" of a function?
The "pre-image" of a function refers to the set of all input values (or elements) that map to a particular output value. In other words, it is the set of all elements in the domain of a function that, when applied to the function, produce a specific output value.
To find the pre-image of a function for a given output value, you can follow these steps:
1. Determine the output value for which you want to find the pre-image.
2. Identify the function that you are working with.
3. Understand the domain of the function, which is the set of all possible input values.
4. Check each element in the domain of the function and apply it to the function.
5. For each input value that maps to the desired output value, add it to the pre-image set.
6. Once you have checked all possible input values, the set of gathered input values is the pre-image of the function for that particular output value.
Keep in mind that some functions may have multiple elements in the pre-image for a single output value, while others may not have any elements at all. Additionally, a function may have multiple output values that correspond to the same pre-image. It all depends on the nature of the function itself.