Understanding Pre-Image in Mathematics | Exploring the Original Set or Figure Before Transformation or Mapping

Pre-image

In mathematics, the term “pre-image” refers to the original or initial set or figure before any transformation or mapping occurs

In mathematics, the term “pre-image” refers to the original or initial set or figure before any transformation or mapping occurs. When discussing functions or transformations, a pre-image is the set of all points or elements that are mapped or transformed into another set or figure using a specific rule or function.

To understand this concept, let’s consider a simple example. Suppose we have a function f(x) = 2x, which multiplies any given number x by 2. If we have a set of numbers A = {1, 2, 3}, the pre-image of A under the function f would be the set of numbers that, when multiplied by 2, give the numbers in A. Thus, the pre-image of A would be {0.5, 1, 1.5}, since each of these numbers, when multiplied by 2, gives us the numbers in A: {1, 2, 3}.

In terms of transformations, a pre-image can be seen as the original shape or figure before any transformation is applied. For instance, let’s consider a triangle and a translation transformation. The pre-image of the triangle would be its initial position before it undergoes any translation. Once the triangle is translated, it becomes the image.

In summary, the pre-image is the set or figure that is transformed or mapped into another set or figure using a specific rule or function. It represents the original state or position before any transformation occurs.

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