1ya f(x) = x2 but then a =4
13 Answers
1i am not getting how does that work because we do not have f(1)
the only good conclusion i got is f(f(1))=1
i also got
f(f(2)=2a
and some silly ones like f(2f(1))=4 f(3f(1)=9 what to do next?
9proof :
f(xf(x) ) =x2+a
f(xf(1) )=x2
let f(1)=λ
f(xλ)=x2
f(x)=(x/λ)2
now f(xf(y))=x2y4/λ4
comparing a=4 λ= ±1
hence f(x) = x2
1how did you get f(x)=(x/λ)2 ???
and the final answer must be f(x)=x2y4
9no shriya see carefully
f(xλ)=x2
f(x)=(x/λ)2 (by replacing x by x/λ )
final ans ive derived see again
and how in the world can f(x) =x2y4 were y is not even involved as a parameter ie( f(x) shud be a function of x alone)
pls think twice before saying someone is wrong :)
1but still f(x)= x2 there shouldn't be any ±
i actually meant f(xf(y))=x2y4
dont be so rude ,,,you should'nt be !!
:) :) :) :)
9/hide]i was not rude i was angry u dint understand wat i was saying( i thought i had explained clearly) still see derivation a subtitute and see for yourself f(x) = -x2 also satisfies
1but you only gave up that f(x)=(x/λ)2 now how is a square going to be negative .... i dont know where are you getting it from but this is what i can say .
btw thank you
9now f(xf(y))=x2y4/λ4 comparing
with x2ya
we get a=4 λ4=1
now λ=±1 hence λ2=1
so f(x) = x2 only
thanks shriya for pointing out the error (ill be more carefull next time)