**MATHMAA**

**Definition of Function:**

A relation in which no two ordered pairs have same first coordinates is called ** function**.

**Domain and Range: **

If f : A→B is a mapping, then A is called the ** domain** of f, B the

__Types of Functions__

**i) One - One function (or injection): ** f:A→B is one - one if f(x1)=f(x2) then x1=x2.

**ii)**** Onto function (or Surjection): A function f:A→B is said to be an onto function. If f(A), the image of A equals B. That is f is onto if every element of B the codomain is the image of atleast one element of A the domain. f:A→B is onto ⇔ for every y∈B there is atleast one x∈A such that f(x) = y ⇔ f(A) = Biii) One-one onto function (Bijection): A function f:A→B is said to be a bijection if it is both one-one and onto.**

**iv)Inverse of a function: **If f is a function then the set of ordered pairs obtained by interchanging the first and second cordinates of each ordered pairs in f and is denoted by f-1 and read as "f-inverse"**v)Identity Function :** A function f:A→B is said to be an identity function on A (denoted by IA) if f(x)=x for all x∈A.

IA is an identity function on A⇔IA(x) = x for all x∈A**vi)Constant Function:** A function f:A→B is a constant function if there is an element c∈B such that f(x) = c for all x∈A.

That is, a constant function is a function whose range is a singleton set.

vii)Equal Function: Two functions f and g defined on the same domain D are said to be equal if f(x)=g(x)

viii)Composite Fuction: Let f:A→B, g:B→C be two functions. Then the composite function of f and g (denoted gof)

gof: A→C is defined by

(gof)(x) = g(f(x)).* Note: * In the product function gof

a) The codomain of f is the domain of g.

b) The domain of gof is the domain of f.

c) The codomain of gof and g is the same set.

d) (gof)(x) = g(f(x)).

*Sample Questions*

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