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Lesson Posted on 28/07/2019 Learn Functions
Practice Problem on Functions for IIT-Mains
Dhanalakshmi N.
Qualification : msc maths Experience : 27 years Teaching boards: cbse, icse, isc , igcse. Teaching...
Lesson Posted on 17/08/2018 Learn Functions
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
Relation means in the real world how closely they know each other
there are many types of relation
Perfect positive relation -very Close
Positive relation -Close to each-other
Negative relation -Apart from each-other
Perfect negative relation -Very apart
If (a,b)∈R,We can say that a is related to b under the relation R
and mathematically it can be written as aRb
Types of Relation
Empty relation
A relation R in set A is called empty relation if no element of A is related to any element of A
i.e. R=Φ⊂AxA
Universal Relation
A relation R in set A is called \universal relation if each element of A is related to every element of A
R=AXA
Both the empty and universal relation are called trivial relation.
A relation R in set A is called.
1) Reflexive if (a,a)∈R,for every a∈R
2)Symmetric if (a,b)∈R implies that (b,a)∈R for all a,b∈A
3)Transitive if (a,b)∈R and (b,c)∈R implies that (a,c)∈R for all a,b,c∈A
A relation R in set A is called an equivalence relation if R is Reflexive, Symmetric and Transitive.
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Lesson Posted on 17/08/2018 Learn Functions
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
The function is nothing but the relation between inputs to the possible outputs, where each input is related to precisely one output.
There are various type of function
1)identity function
2)Constant function
3)polynomial function
4)Rational Function
5)Modulus function
6)Signum Function
A function f:x→y is defined to be a One-one or injective function if images of a distinct element of X under f are distinct
for every x1 and x2 ∈ X f(x1)=f(x2)
implies x1=x2
otherwise, function f is called many-one
A function f:x→y is defined to be an On-to or surjective function
if every element of Y is an image of some element of X under function f
for every y∈Y,there exist an element x in X such that f(x)=y
A function f:x→y is said to be one-one and onto (or bijective), if f is both one-one and onto.
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Lesson Posted on 17/08/2018 Learn Functions
Continuous and discontinuos function
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
Continuous function:
If there are no gaps in the curve or no breakpoint in the curve are called the continuous function
for example f(x)=x2 is continuous function
Discontinuous function:
If there are gaps in the curve or breakpoint in the slider are called the continuous function
f(x)=1/x-1 is discontinuous function
read lessAnswered on 22/11/2016 Learn Functions
Chandan Singh
Tutor
Asked on 03/11/2016 Learn Functions
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Asked on 03/11/2016 Learn Functions
Asked on 03/11/2016 Learn Functions
Asked on 03/11/2016 Learn Functions
Take Tuition from the Best Tutors
Asked on 03/11/2016 Learn Functions
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