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Category: Relation and Functions

f-x-1-x-x-6-1-27-f-x-

Question Number 12386 by Joel576 last updated on 21/Apr/17 $${f}\left({x}\:+\:\frac{\mathrm{1}}{{x}}\right)\:=\:\frac{{x}^{\mathrm{6}} \:+\:\mathrm{1}}{\mathrm{27}} \\ $$$${f}\left({x}\right)\:=\:? \\ $$ Answered by ajfour last updated on 21/Apr/17 $${let}\:\:\left({x}+\frac{\mathrm{1}}{{x}}\right)={t} \\ $$$${since}\:\:\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}}…

let-f-x-arctan-2-x-2-1-calculate-f-n-x-and-f-n-0-2-if-f-x-a-n-x-n-find-the-sequence-a-n-

Question Number 143381 by Mathspace last updated on 13/Jun/21 $${let}\:{f}\left({x}\right)={arctan}\left(\sqrt{\mathrm{2}}{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right){and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){if}\:{f}\left({x}\right)=\Sigma{a}_{{n}} {x}^{{n}} \:\:{find}\:{the}\: \\ $$$${sequence}\:{a}_{{n}} \\ $$ Answered by…