Question Number 84627 by M±th+et£s last updated on 14/Mar/20
![1)∣sec(x)∣<2tan(x) on[0,2π] 2)find the cirtical points and the range of f(x)=∣x−3∣+∣2x+1∣](Q84627.png)
$$\left.\mathrm{1}\right)\mid{sec}\left({x}\right)\mid<\mathrm{2}{tan}\left({x}\right)\:{on}\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$ $$ \\ $$ $$\left.\mathrm{2}\right){find}\:{the}\:{cirtical}\:{points}\:{and}\:{the}\:{range}\:{of} \\ $$ $${f}\left({x}\right)=\mid{x}−\mathrm{3}\mid+\mid\mathrm{2}{x}+\mathrm{1}\mid \\ $$ $$ \\ $$
Commented byTANMAY PANACEA last updated on 14/Mar/20
$${what}\:{is}\:{wuestion}\:{no}\:\mathrm{1} \\ $$
Commented byM±th+et£s last updated on 14/Mar/20
$${solve}\:{the}\:{inequality} \\ $$
Answered by TANMAY PANACEA last updated on 14/Mar/20
$$\left.\mathrm{2}\right)\:{f}\left({x}\right)=\mid{x}−\mathrm{3}\mid+\mid\mathrm{2}{x}+\mathrm{1}\mid \\ $$ $${critical}\:{value}\:{of}\:{x}\:{are}\:\mathrm{3},−\mathrm{0}.\mathrm{5} \\ $$ $${f}\left({x}\right)\:={x}−\mathrm{3}+\mathrm{2}{x}+\mathrm{1} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3}{x}−\mathrm{2}\:\:\:\:\:{when}\:{x}>\mathrm{3} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{7}\:\:\:\:\:\:\:{when}\:{x}=\mathrm{3} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:=−\left({x}−\mathrm{3}\right)−\left(\mathrm{2}{x}+\mathrm{1}\right)\:\:\:{x}<−\mathrm{0}.\mathrm{5} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:\:=−\mathrm{3}{x}+\mathrm{2} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3}.\mathrm{5}\:\:\:{when}\:{x}=−\mathrm{0}.\mathrm{5} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:\:=−\left({x}−\mathrm{3}\right)+\mathrm{2}{x}+\mathrm{1}\:\:\:{when}\:\:\mathrm{3}>{x}>−\mathrm{0}.\mathrm{5} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:={x}+\mathrm{4} \\ $$ $${so}\:{f}\left({x}\right)\in\left[\mathrm{3}.\mathrm{5},\infty\right) \\ $$ $$ \\ $$ $$ \\ $$
Commented byjagoll last updated on 14/Mar/20
