Mathematics : Relation and Function: Points to Remember

**Points to Remember**

**• **The Cartesian Product of** ***A*** **with** ***B*** **is defined as** ***A*** **×** ***B*** **=** **{(*a*** **,** ***b*)** **| for all *a*** **∈** ***A*,** ***b *∈* B*}

**• **A relation R from** ***A*** **to** ***B*** **is always a subset of** ***A*** **×*B*** **. That is** **R** **⊆** ***A*** **×*B*

**• **A relation R from** ***X*** **to** ***Y*** **is a function if for every** ***x*** **∈** ***X*** **there exists only one *y*** **∈*Y*** **.

**• **A function can be represented by

(i) an arrow diagram

(ii) a tabular form

(ii) a set of ordered pairs

(iv) a graphical form

**• **Some types of functions

(i) One-one function

(ii) Onto function

(iii) Many-one function

(iv) Into function

**• **Identity function** ***f*** **(*x*** **)** **=** ***x*

**• **Reciprocal function** ***f*** **(*x*** **)** **=** 1/***x*^{}

**• **Constant function** ***f*** **(*x*** **)** **=** ***c*

**• **Linear function** ***f*** **(*x*)** **=** ***ax*** **+*b*** **,** ***a*** **≠** **0

**• **Quadratic function** ***f*** **(*x*** **)** **=** ***ax*** **^{2}** **+*bx*** **+*c*** **,** ***a*** **≠** **0

**• **Cubic function** ***f*** **(*x*** **)** **=** ***ax*** **^{3}** **+*bx*** **^{2}** **+** ***cx*** **+*d*** **,** ***a*** **≠** **0

**• **For three non-empty sets** ***A*,** ***B*** **and** ***C*, if
*f *:* A *→*
B *and* g *:* B *→* C *are two* *functions, then the composition of *f* and *g* is a function *g f* : *A* → *C*
will be defined as *g o f* (*x* ) = *g*(
*f* (*x* )) for all *x* ∈ *A*
.

**• **If** ***f*** **and** ***g*** **are any two functions,
then in general,** ***f **o g*** **≠** ***g **o
f*** **

**• **If** ***f*,** ***g*** **and** ***h*** **are any three functions,
then** ***f*** ***o* (*g **o h*** **)** **=** **(** ***f **o g*** **)** ***o h*

Tags : Relation and Function | Mathematics , 10th Mathematics : UNIT 1 : Relation and Function

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10th Mathematics : UNIT 1 : Relation and Function : Points to Remember | Relation and Function | Mathematics

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