Understanding Image and Inverse Image in Functions

This video tutorial introduces the concepts of image and inverse image in the context of functions. It explains how to denote the image of an element from the domain in the codomain and how to find the image of a subset of the domain. The tutorial also covers the inverse image, which identifies elements in the domain that map to a specific element in the codomain. Through examples, the video demonstrates how to use special notation to simplify these concepts, providing a clear understanding of how functions map elements between domains and codomains.

What is the notation used to represent the image of an element x in the domain?

• f(y)

• x(f)

• y(f)

• f(x)

When discussing functions, what is the term for the set of all images of elements in a subset of the domain?

• Image Set

• Inverse Image

• Domain Set

• Codomain Set

In the example provided, what is the image of the set with elements 1, 2, and 3?

• {11, 15}

• {17}

• {1, 2, 3}

• {5}

What is the notation used to denote the inverse image of a subset B under a function f?

• B(f)

• f^-1(B)

• f(B)

• B^-1(f)

If a particular element y in the codomain is not in the range, what is the inverse image of the set containing y?

• The set containing y

• The set containing y and all elements of the domain

• The empty set

• The set containing all elements of the domain

What happens if a function is not injective regarding the inverse image?

• Multiple elements may map to the same element in the codomain

• Each element in the domain maps to a unique element in the codomain

• The inverse image is always empty

• No elements map to any element in the codomain

In the example, what is the inverse image of the set with elements 11 and 15?

• {1, 2, 3, 4}

• {17}

• {5}

• {11, 15}

In the final example, what is the inverse image of the set with the element d?

• The empty set

• The set with elements a, b, c, d

• The set with elements 1, 2, 3, 4, 5

• The set with element d

What is the image of the set with elements 1, 2, and 3 under the function f in the last example?

• {a, b}

• {c, d}

• {1, 2, 3}

• {a, c}

In the last example, which elements from the domain have images of a or b?

• {1, 2, 3, 4, 5}

• {4, 5, 6}

• {2, 3, 4}

• {1, 2, 3}