find-all-continous-functions-f-R-R-such-that-f-x-2-1-f-1-x-4-x-R-

Question Number 151453 by mathdanisur last updated on 21/Aug/21

find all continous functions f : R \to R

such that :

f (x^{2} + 1) = f (\sqrt{1 + x^{4}}); \forall x \in R

Commented by MJS_new last updated on 21/Aug/21

f (x) = c \land c \in R

Commented by mathdanisur last updated on 21/Aug/21

wrong

Commented by MJS_new last updated on 21/Aug/21

no . maybe there are other functions . but with

f (x) = c : f (x^{2} + 1) = f (\sqrt{x^{4} + 1}) = c

Commented by mathdanisur last updated on 22/Aug/21

need to prove

Commented by MJS_new last updated on 22/Aug/21

sorry but what do you want to prove ?

f (x) = 5 \Rightarrow f (x^{2} + 1) = f (\sqrt{x^{4} + 1}) = f (\frac{x^{37} + 3 \ln (x^{2} + 2)}{{5 e}^{i x} + 9 ζ (33)}) = 5

Commented by mathdanisur last updated on 22/Aug/21

p l e a s e s o l v e a g a i n, t h a n k s

Commented by MJS_new last updated on 22/Aug/21

this is weird

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