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Sahithyan's S1
Sahithyan's S1 — Mathematics

Functions

A function f:ABf:\,A\rightarrow{B} is a relation f:ABf:\,A\rightarrow{B} which is everywhere defined and not one-many.

  • dom(f)=A=preran(f)dom(f)=A=preran(f)

Inverse

For a function f:ABf:\,A\rightarrow{B} to have its inverse relation f1:BAf^{-1}:\,B\rightarrow{A} be also a function:

The above statement is true for all unrestricted function ff that has an inverse f1f^{-1}:

f(f1(x))=x=f1(f(x))=xf(f^{-1}(x))=x=f^{-1}(f(x))=x

Real-valued functions

When both domain and codomains of a function are subsets of R\mathbb{R}, the function is said to be a real-valued function.

Odd and Even functions

Odd function

A function ff that is f(x)=f(x)  xDom(f)f(-x)=-f(x)\; \forall x \in \text{Dom}(f).

Even function

A function ff that is f(x)=f(x)  xDom(f)f(-x)=f(x)\; \forall x \in \text{Dom}(f).