Functions and Continuity
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Image set
Equations are omitted for technical reasons - download the original pdf
We may wish to know what the image of a subset A of the domain of a function is. The image of a set A under the function f is the set of all values to which elements in A are mapped by f. The symbol [symbol] is used to denote this set and is defined as [Equation goes here - download the original pdf to see it.] We add the proviso that [symbol] must be defined for all values [symbol]. For example, the function [Equation goes here - download the original pdf to see it.] does not take a value when x = 0, because that is equivalent to dividing by zero. Example (10) Find the image under f of the set A given by interval [Equation goes here - download the original pdf to see it.] when [Equation goes here - download the original pdf to see it.] . [Example goes here - download the original pdf to see it.]
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Contents of
Functions and Continuity
1 Functions
2 Graph
3 Inverse of a Function: monotone increasing or decreasing functions
4 The reciprocal function - singularities
5 Functions defined piecewise on their domain
6 Limits
7 Formal definition of a limit
8 Formal definition of the limit of a function at a point x = a
9 Informal arguments
10 Continuity
11 Combining limits
12 Quotients
13 Image set
14 Inverse image
15 Odd and even functions
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