Question

questão de função, segue o anexo abaixo

Answer 1

Explicação passo-a-passo:

Calculando a função inversa de f(x):

$y=f(x)\\\\y=\dfrac{3x+k}{-3x+6} \\\\\text Realizando\ a\ invers\~{a}o\ de\ x\ e\ y:\\\\x=\dfrac{3y+k}{-3y+6}\\\\\text Isolando\ o\ y:\\\\x.(-3y+6)=3y+k\\\\-3xy+6x=3y+k\\\\-3xy-3y=k-6x\\\\y.(-3x-3)=k-6x\\\\y=\dfrac{k-6x}{-3x-3} \\\\\boxed{f^{-1}(x)= \dfrac{k-6x}{-3x-3}}$

Sabemos que $f^{-1} (-2)=4$.

$f^{-1}(-2)= \dfrac{k-6.(-2)}{-3.(-2)-3}\\\\ \dfrac{k-6.(-2)}{-3.(-2)-3}=4\\\\\dfrac{k+12}{6-3}=4\\\\ \dfrac{k+12}{3}=4\\\\k+12=4.3\\\\k+12=12\\\\k=12-12\\\\\boxed{\boxed{k=0}}$