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f-x-x-2-6x-f-1-x-

Question Number 192076 by sciencestudentW last updated on 07/May/23 $${f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{6}{x}\:\:\:\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$ Answered by AST last updated on 07/May/23 $${y}={f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{6}{x}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{9} \\…

x-1-x-2-dx-

Question Number 126520 by joki last updated on 21/Dec/20 $$\int\frac{\mathrm{x}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}\:} \:\:}}\mathrm{dx} \\ $$ Answered by liberty last updated on 21/Dec/20 $$−\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{{d}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:=\:−\frac{\mathrm{1}}{\mathrm{2}}\int\:\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{−\frac{\mathrm{1}}{\mathrm{2}}} \:{d}\left(\mathrm{1}−{x}^{\mathrm{2}}…

fog-x-4x-1-g-x-x-2-f-x-

Question Number 192049 by sciencestudentW last updated on 06/May/23 $${fog}\left({x}\right)=\mathrm{4}{x}−\mathrm{1} \\ $$$${g}\left({x}\right)={x}−\mathrm{2} \\ $$$${f}\left({x}\right)=? \\ $$ Answered by AST last updated on 06/May/23 $${f}\left({g}\left({x}\right)\right)=\mathrm{4}{x}−\mathrm{1}\Rightarrow{f}\left({x}−\mathrm{2}\right)=\mathrm{4}\left({x}−\mathrm{2}\right)+\mathrm{7} \\…

if-the-combined-function-is-h-x-3x-2-1-then-find-the-tow-other-functions-of-its-

Question Number 192048 by sciencestudentW last updated on 06/May/23 $${if}\:{the}\:{combined}\:{function}\:{is}\:{h}\left({x}\right)=\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${then}\:{find}\:{the}\:{tow}\:{other}\:{functions}\:{of}\:{its}. \\ $$ Commented by AST last updated on 07/May/23 $${If}\:“{combined}''\:{here}\:{means}\:{h}\left({x}\right)={f}\left({g}\left({x}\right)\right), \\ $$$${f}\left({x}\right)=\sqrt{{x}},{g}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}}…