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Category: Relation and Functions

Question-164176

Question Number 164176 by mathlove last updated on 15/Jan/22 Answered by mr W last updated on 15/Jan/22 $${f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)={x}\:\:\:\:…\left({i}\right) \\ $$$${replace}\:{x}\:{with}\:\mathrm{1}−\frac{\mathrm{1}}{{x}} \\ $$$$\Rightarrow{f}\left(\frac{{x}−\mathrm{1}}{{x}}\right)+{f}\left({x}\right)=\mathrm{1}−\frac{\mathrm{1}}{{x}}\:\:\:…\left({ii}\right) \\ $$$${replace}\:{x}\:{with}\:\frac{\mathrm{1}}{\mathrm{1}−{x}} \\…

Let-f-N-R-be-a-function-sarisfying-following-conditions-f-1-1-f-1-2f-2-nf-n-n-n-1-f-n-Then-find-the-value-of-49f-49-

Question Number 33048 by rahul 19 last updated on 09/Apr/18 $${Let}\:{f}:{N}\rightarrow{R}\:{be}\:{a}\:{function}\:{sarisfying} \\ $$$${following}\:{conditions}: \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1}. \\ $$$${f}\left(\mathrm{1}\right)+\mathrm{2}{f}\left(\mathrm{2}\right)+….+{nf}\left({n}\right)={n}\left({n}+\mathrm{1}\right){f}\left({n}\right). \\ $$$${Then}\:{find}\:{the}\:{value}\:{of}\:\mathrm{49}{f}\left(\mathrm{49}\right)\:? \\ $$ Commented by rahul 19…

If-range-of-f-x-x-1-x-2-x-3-x-4-5-x-6-6-is-a-b-a-b-N-find-a-b-

Question Number 33036 by rahul 19 last updated on 09/Apr/18 $${If}\:{range}\:{of}\: \\ $$$${f}\left({x}\right)=\:\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)\left({x}+\mathrm{4}\right)+\mathrm{5} \\ $$$${x}\in\:\left[−\mathrm{6},\mathrm{6}\right]\:{is}\:\left[{a},{b}\right]\:,{a},{b}\in{N},\:{find}\:{a}+{b}\:? \\ $$ Answered by MJS last updated on 09/Apr/18 $$\mathrm{we}\:\mathrm{need}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{and}…