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f-x-1-x-x-2-x-x-2-is-given-D-f-domain-R-f-range-

Question Number 206328 by mnjuly1970 last updated on 12/Apr/24 $$ \\ $$$$\:\:\:\:\:\:\:{f}\left({x}\right)=\:\lfloor\:\frac{\:\mathrm{1}+\:{x}\:+{x}^{\mathrm{2}} }{{x}+\:{x}^{\:\mathrm{2}} }\:\rfloor\:{is}\:{given}. \\ $$$$\:\:\:\:\:\:\:\Rightarrow\begin{cases}{\:\:{D}_{{f}} \:=\:?\:\left({domain}\:\right)}\\{\:\:\:{R}_{\:{f}} \:=\:?\left(\:{range}\right)}\end{cases} \\ $$$$ \\ $$ Answered by TheHoneyCat…

If-0-lt-a-lt-1-Compare-1-a-1-a-a-1-1-1-a-a-1-a-a-2a-

Question Number 206363 by hardmath last updated on 12/Apr/24 $$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}<\mathrm{1} \\ $$$$\mathrm{Compare}: \\ $$$$\frac{\mathrm{1}}{\mathrm{a}−\mathrm{1}}\:\:,\:\:\frac{\mathrm{a}}{\mathrm{a}−\mathrm{1}}\:\:,\:\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{a}}\:\:,\:\:\frac{\mathrm{a}}{\mathrm{1}−\mathrm{a}}\:\:,\:\:\frac{\mathrm{a}}{\mathrm{2a}} \\ $$ Commented by TheHoneyCat last updated on 12/Apr/24 Commented by…

Question-206353

Question Number 206353 by BaliramKumar last updated on 12/Apr/24 Commented by Rasheed.Sindhi last updated on 15/Apr/24 $${I}\:{think}\:\mathrm{15}\:{is}\:{wrong}\:{here},\:{it}\:{should} \\ $$$${be}\:\mathrm{14}\:{or}\:{otherwise}\:{the}\:{answer}\:{is} \\ $$$${not}\:{correct}. \\ $$ Commented by…

If-abc-1-then-prove-that-1-1-a-b-1-1-1-b-c-1-1-1-c-a-1-1-

Question Number 206322 by MATHEMATICSAM last updated on 12/Apr/24 $$\mathrm{If}\:{abc}\:=\:\mathrm{1}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{a}\:+\:{b}^{−\mathrm{1}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{b}\:+\:{c}^{−\mathrm{1}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{c}\:+\:{a}^{−\mathrm{1}} }\:=\:\mathrm{1} \\ $$ Commented by Rasheed.Sindhi last updated on 12/Apr/24 $${For}\:{similar}\:{question}\:{see}…

if-the-sum-of-three-positive-real-numbers-is-equal-to-their-product-prove-that-at-least-one-of-the-numbers-is-larger-than-1-7-

Question Number 206355 by mr W last updated on 12/Apr/24 $${if}\:{the}\:{sum}\:{of}\:{three}\:{positive}\:{real}\: \\ $$$${numbers}\:{is}\:{equal}\:{to}\:{their}\:{product}, \\ $$$${prove}\:{that}\:{at}\:{least}\:{one}\:{of}\:{the}\: \\ $$$${numbers}\:{is}\:{larger}\:{than}\:\mathrm{1}.\mathrm{7}. \\ $$ Answered by A5T last updated on…