Function in terms of relation - Relations & Functions Video Lecture - Class 12

hello friends this video on relations
and functions part 1 is brought to you
by exam feel calm no more fear from
exams topics to be covered relation and
functions in relation and functions will
cover relation and function overview
Cartesian product offsets relations in
terms of product offsets function in
terms of product of sense functions in
terms of relations real and real valued
functions graphs algebra of functions
relation what is relation relation is a
connection between or among things for
example when I say relation between
father mother and child this is the
relation relation between has been a
pipe
there's the relation also note that
every relation has a pattern and every
relation involves minimum to identity
let me explain things once again when I
say that father and mother there is a
relation between father mother if we
include a child also there is a relation
between father mother and child this is
the relation between father and child
mother and child mother than shine
similarly when you say husband and wife
there is a relationship we know that a
husband and I behave in a different way
there's a relationship between husband
and wife when I see student student and
teacher here also business relationship
there's a relationship between student
and teacher and that relationship is
that we should teach the student father
mother takes care of child
similarly husband and wife they together
build their family let me reiterate what
I have said relation is nothing
a connection connection between or among
things but it is to object when we sit
we see between when it has been more
than two object we say among for example
father mother and child so it is a
relationship among three people when I
see husband and wife we see relationship
between husband and wife and we need to
note that even relation has a pattern of
property husband and wife has a partner
student test and teacher has a pattern
similarly father mother inside as a
pattern also for a relation to exist it
should have minimum two identity I can't
say husband has a relation even I say
only husband that make sense you say
that husband has a relation I should say
husband relationship with with five or
with kid you need to have minimum two
identity or relation to existence this
is the basic idea of relation we'll
explore more in the future chapters now
let's see what does relation me in
mathematical world there are some
examples of relation mathematical world
if you say number P is greater than Q
you say number P is greater than Q is an
example of relationship fine because
they are more than one identity P and Q
and there's a pattern the pattern is all
the number in P is greater than Q for
example four is greater than five so P
is part of four sorry five is greater
than 4 so we'll say P is part of five
and Q is part of whole similarly when we
say line m is perpendicular to line and
this is line in and this is line him so
there are two lines they are
perpendicular here also we see there are
two identities involved that is line MN
line in and there is a property the
properties that hold the lines are
perpendicular so this is also an example
of relation when we say a is a subset of
B this is a set and this is a bigger set
B so when you say is a subset of B here
also we see there are two elements in
Bond env and this is a pattern the
pattern is that a is subset of D for
example
in a right triangle we have P B and H
that this is a right triangle so we say
according to Pythagoras theorem that v
square plus v square into S square
mention here so this is also a
relationship with PB NH it involves PB
image 3 identity and there is a pattern
that p square plus v square is going to
match so these are some examples of the
relation so what is function function is
nothing but the set of action or
activity
let me repeat function is a set of
action or activity we'll take an example
let's suppose Phyllis is a function so
here let's create fullest as a function
do this for this when I pass criminal as
input what it does it sends up for a
little 2j the same poulos if I pass good
citizen as input what it does it send
that person to home so you see the same
polis is behaving differently depending
on the person it is in then Kramer comes
to police police catch the criminal and
sent to jail when a good citizen comes
to police it sends the good citizen do
so so Pulis is nothing but a set of
action for example when we police find
the criminal it'll catch the kernel
it'll put some in entering the police
registry and then put the person in the
jail so it is performing some action and
the output is jail similarly let's take
one more example which is relevant to
you guys because you are not interacting
with full as much so let's suppose we
have a teacher teacher is a function
so in the exam if you give good answer
or if you give right answer if you give
correct answer the teacher gives you
good score correct good score a plus but
when you give an incorrect answer
incorrect answer the same teacher gives
you bad score correct teacher is also a
function here so depending on the input
this is all left sides input and right
side is the output depending on the
input you are giving whether you are
giving correct answer you're giving any
correct answer the teacher is giving you
good score and bad score similarly in
case of Perez depending on whether
Phyllis is getting a criminal or citizen
who is behaving in different way this is
a very very very basic overview of
function function is nothing but a set
of action to be performed we can
consider the function as a box and then
we can give an input to get the output
let us take example of a rapidity
formation where input from one function
goes to another function so here let's
take one more function called parents p
r e and t so you gave a correct answer
to the teacher t shall give you good
score you gave a good score to pinch you
sure to do you got a good score
you got blessings and you get gifts from
pins correct you gave a bad answer or
incorrect as a teacher T shall give you
bad score you showed the bad score to
your parents what you got from parents
scolding correct so this is an example
of where input from one function is
going to another function so in this
case we say Peleus teacher parents are
all acting as a function let's see
function in mathematics world
example we have FX is equal to x squared
so let's assume this is a function I'll
create a bigger one and this function is
FX is going to do X square so whatever
the input you give it squares example
that if you give one is important what
you get is one square that is 1 then if
you do is input you get 2 square that is
4 and if you 3 as input to this function
you get 3 square that is 9 and if you
food as input is function what you get 4
squared is 16
then you fight this input is function
you get 5 square that is 25
similarly if you give a negative number
for example you give name minus 3 so
minus 3 whole square is 9 this is the
function which squares the input this is
input and this is output so if you give
minus 2 as input you get minus 2 square
is equal to 4 so this is a typical
example of function in mathematics 1
whatever input you give it squares the
input and gives you oh let us discuss
what is liam m3 and valid function real
value function is a function for which
range is real number that is the output
is real the output is real the input may
not be real the input is not realizable
so it is real valued function real
valued function and when I say real
function so in that case both input and
output is yeah that is both the range
and domain of example of Regal function
FX is equal to X to the power 4 you say
you give a real input here 1 you get for
output 1 output you give 2 input here 2
to the power 4 for 16 as output this
example of real function very input is
real or not goodness for real value
function the input is not real it is not
real
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