Question

determine os valores reais de m de mode que sejá possivel a igualdade de sen x = 4m - 2? me ajudeeem por favor!

Answer 1

$\mathrm{f(x)=\sin{x}\ \to\ \boxed{\mathrm{f(x)=[-1,1]\ ou\ -1\leq f(x)\leq1}}}\\\\ \mathrm{*\ \sin{x}=4m-2}\\\\ \textbf{Condi\c{c}\~oes de exist\^encia:}\\\\ \mathrm{-1\leq4m-2\leq1\ \to\ -1+2\leq4m-2+2\leq1+2}\\\\ \mathrm{1\leq4m\leq3\ \to\ \dfrac{1}{4}\leq\dfrac{4m}{4}\leq\dfrac{3}{4}\ \to\ \boxed{\mathbf{\dfrac{1}{4}\leq m\leq\dfrac{3}{4}}}}$