functional eqn
If f(x)+f(y)+f(xy)=2+f(x)f(y) for all x, y in R and f(x) is a polynomial function with f(4)=65 then find the value of f(5) if f(1) =/= 1
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@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.i was able to get f(1)= 2
after that nothing meaningul
In funtional equation questions try putting x=y or x=1/y or differentiating after you get some values
In this ques x=1/y should work ig
Because you will get f(1) and you will have a relation in one variable
X=y doesn't give something meaningful
X=1/y gives f(x)f(1/x) = f(x) + f(1/x)
Is the answer 18?
i got fx=x^3+1 by intuition but dk the proper method
oh wait right its 18
Oh wait, this is incomplete 🤦♂️
Alr understandable but not doable in exam
Cant we do something with this
The second image is irrelevant if you remember the result for f(xy)=f(x).f(y) but yea...
You'll prolly have to partial differentiate in exam.
Which I don't do and it costs me humongous loss of time :/
Actually once you get used to algebra the first 4 lines give you the idea of the answer though tbh.
can u share some general functional eqns and their solutions
also the general soln of f(x)f(y)=f(x)+f(y) is f(x)=alnx+c
putting f(1)= 2 gives c=2 , f(4)=65 gives a= 63/ln4 . f(5) is just wrong then
its given fx is a polynomial function so well have to reject this one
oh han
so direct alternate soln nahi milta koi?
idk...havent tried it yet
It is aln(x) for that one. And here we have g(xy)=g(x).g(y) though.
i was talking bout the eqn obtained by putting y=1/x
Will do as soon as I get some paper.
lmao 😭
Yeah you can send everything to the otherside and do what lance did
why not find f (1) then put x=1,y =5?
On I got it why...
mila??
we good?
+solved @SirLancelotDuLac
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