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

$$\mathrm{find}\mathrm{all}\mathrm{continous}\mathrm{functions}\mathrm{f}:\mathbb{R}\to \mathbb{R}$$$$\mathrm{such}\mathrm{that}:$$$$\mathrm{f}({\mathrm{x}}^2+1)=\mathrm{f}\left(\sqrt{1+{\mathrm{x}}^4}\right);\mathrm{\forall }\mathrm{x}\in \mathbb{R}$$

Commented by MJS_new last updated on 21/Aug/21

$$f\left(x\right)=c\wedge c\in \mathbb{R}$$

Commented by mathdanisur last updated on 21/Aug/21

$$\mathrm{wrong}$$

Commented by MJS_new last updated on 21/Aug/21

$$\mathrm{no}.\mathrm{maybe}\mathrm{there}\mathrm{are}\mathrm{other}\mathrm{functions}.\mathrm{but}\mathrm{with}$$$$f\left(x\right)=c:f(x^2+1)=f\left(\sqrt{x^4+1}\right)=c$$

Commented by mathdanisur last updated on 22/Aug/21

$$\mathrm{need}\mathrm{to}\mathrm{prove}$$

Commented by MJS_new last updated on 22/Aug/21

$$\mathrm{sorry}\mathrm{but}\mathrm{what}\mathrm{do}\mathrm{you}\mathrm{want}\mathrm{to}\mathrm{prove}?$$$$f\left(x\right)=5\Rightarrow f(x^2+1)=f\left(\sqrt{x^4+1}\right)=f\left(\frac{x^{37}+3\ln (x^2+2)}{{5\mathrm{e}}^{\mathrm{i}x}+9\zeta \left(33\right)}\right)=5$$

Commented by mathdanisur last updated on 22/Aug/21

$$pleasesolveagain,thanks$$

Commented by MJS_new last updated on 22/Aug/21

$$\mathrm{this}\mathrm{is}\mathrm{weird}$$

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