Functions
1.0 Definitions
2.0 Relation
3.0 Types of Relation
4.0 Functions
5.0 Standard Real Functions and their Graphical Representation
5.10 Reciprocal Function
5.1 Constant Function
5.2 Identity Function
5.3 Modulus Function
5.4 Greatest Integer Function or Floor Function
5.5 Smallest Integer Function or Ceiling Function
5.6 Fractional Part Function
5.7 Signum Function
5.8 Exponential Function
5.9 Logarithmic Function
5.11 Square Root or Radical Function
5.12 Square Function
5.13 Cube Function
5.14 Cube Root Function
6.0 Operations on Real Functions
7.0 Types of Functions
8.0 Composition of a Function
9.0 Inverse of a Function
8.1 Properties of Composition of a Function
5.1 Constant Function
5.2 Identity Function
5.3 Modulus Function
5.4 Greatest Integer Function or Floor Function
5.5 Smallest Integer Function or Ceiling Function
5.6 Fractional Part Function
5.7 Signum Function
5.8 Exponential Function
5.9 Logarithmic Function
5.11 Square Root or Radical Function
5.12 Square Function
5.13 Cube Function
5.14 Cube Root Function
Property 1: The composition of functions is not commutative. $$fog \ne gof$$
Property 2: The composition of functions is associative, i.e. if $f$, $g$ and $h$ are three functions such that $(fog)oh$ and $fo(goh)$ exists, then $$(fog)oh = fo(goh)$$
Property 3: Let $f:A \to B$ and $g:B \to A$ be two functions where, $gof = {I_A}$ , then $f$ is an injection and $g$ is a surjection. Similarily, if $fog = {I_B}$, then $f$ is a surjection and $g$ is an injection.
