Relations and Functions Examples (NCERT) (Part -3) Video Lecture | Mathematics (Maths) Class 12 - JEE

hello friends this video on relations
and functions par 29 is brought you by
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before watching this video please make
sure that you have watched part 1 - Part
3 D 8 let us take one more example
similar to one same version it says that
F of G sorry gof is Anto and the
question is whether F ng aren't or not
this gof is ando we have to tell whether
G and F are on DoDEA's or not there is a
big question market G Oprah's honor is
given we have done whether F and G are
on the wall similar so if F G yo f is on
don't so let's take this kind of gnarly
rare this is my H function is my G
function I don't have one two three
mapping went to clean up being only
alright let's have one two three mapping
like this so if you see this this whole
set which I'm talking about is on the
function alright now we can make these
functions on Honda also pokum so if we
have some extra element for here let's
suppose if you see this this is becomes
normal
because if you even if you add extra
element five here this will not impact
this system the system will still have
this number this is a B and if you see
let's suppose from A to C they still
have the composite function will be
still have these numbers only want to
keep on cleanly even if you add more
limited you see here you're adding more
element NV this is not on them
epic overcome this is on them because
there is no experiment here so thus we
can see that if gof is on though it does
not necessarily mean that both G and F
has to be on F can be non Anto also this
is one scenario if you see we have got
this a bigger system for me to see
which is on top but a to be is not Honda
must know something it can be verified
instead of that if gof is one one if if
gof is one one if this implies F is one
ago and G need not be much higher if Gio
F is on tow this implies G is Ponte this
is what he explained in the last
chapters also curry last like so if you
see here what we have done
Gio is one one then G so f is 1 1 G need
not be 101 current jihad is 101 F should
be one on cheating on me 1 1 so you
ready in this case if my gf is on tow
then G has to wear for every not be on
this general statement is my G of is 101
that means F is 101 and geo is on 2 that
means Jesus on the please memorizers
this is a function I have from 1 2 3 to
ABC so f function we will define like
this 1 2 3 2 easy see the points first
and we say F 1 is going to be F 2 is
equal to B and F 3 is going to see this
is my function f you have to prove that
there exists a function G that is from
ABC to 1 2 3 the mapping is still not
known plus there exists a function G
such that G oh f is equal to PI X and F
G is equal to ry right where X is
nothing but 1 2 3 2 this becomes 1 2 3
and this is anyways a visit
for geo F is nothing but G of FX if you
see correct so if I want to find if you
give input as 1 this becomes G of F 1
and this becomes G of a correct and G
this is G function G of a is not a
defined to have some value n right and G
of F 2 will become G of B and G of F 3
will become G of C the value is still
not defined because the mapping is not
done here
now the question says the question see
is that you have to prove that there
exists a function G such that G of F is
equal to IX so this this gof should be
equal to IX that tell it should have
value 1 2 n 3 obviously if you see right
this will have this value only correct
why because if you do this mapping here
it's probably do this in this kind of
having a if this kind of mapping is done
so G of a is 1 B is 2 and G of C is 3 so
if you see G of FX if you see G or F is
something but I X Y because these
numbers are 1 2 3 a part of X so G of F
become IX similarly wanted 9f on G this
is nothing world F of G X now you give
first input as a because this is the
input as ABC here this is G function so
f of G a is 1 input F of G V is another
input and F of G sees in G of a again is
f of 1 because G of a is 1
this becomes F of 2 and this becomes F
of C F of 1 is how much a this is V you
see you see F of G is nothing but ABC
sent this is y so we can say that F of G
is thus we have proved that there exists
a function G where G is 1 GB is 2 and G
C 3 says that gof is IX and F of G is PI
Y all right and that is something which
we have see in this portion the function
for function f the mapping was given for
function G the domain and codomain was
given but the mapping was not we told
that you to prove that there is this one
function G such that G of is IX and F of
G is so when I got this G of X I caught
this values what F of G I got this
Lalo's just made this random happy you
can make any nothing that should be 101
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