Question

a) Determine o valor de k.
b) Calcule o valor de g(-3) • g(-2) • g(1).

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{g(x) = \left(\dfrac{1}{k}\right)^x}$

$\mathsf{D_Y = g(-4) = \left(\dfrac{1}{k}\right)^{-4} = k^4}$

$\mathsf{C_Y = g(-2) = \left(\dfrac{1}{k}\right)^{-2} = k^2}$

$\mathsf{S = \dfrac{(B + b)\:.\:h}{2}}$

$\mathsf{6 = \dfrac{(k^4 + k^2)\:.\:\not2}{\not2}}$

$\mathsf{k^4 + k^2 - 6 = 0}$

$\mathsf{y = k^2}$

$\mathsf{y^2 + y - 6 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = 1^2 - 4.1.(-6)}$

$\mathsf{\Delta = 1 + 24}$

$\mathsf{\Delta = 25}$

$\mathsf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-1 \pm \sqrt{25}}{2} \rightarrow \begin{cases}\mathsf{y' = \dfrac{-1 + 5}{2} = \dfrac{4}{2} = 2}\\\\\mathsf{y'' = \dfrac{-1 - 5}{2} = -\dfrac{6}{2} = -3}\end{cases}}$

$\boxed{\boxed{\mathsf{k = \sqrt{2}}}}$

$\mathsf{g(-3)\:.\:g(-2)\:.\:(g(-1) = \left(\dfrac{1}{\sqrt{2}}\right)^{-3}\:.\:\left(\dfrac{1}{\sqrt{2}}\right)^{-2}\:.\:\left(\dfrac{1}{\sqrt{2}}\right)^{-1}}$

$\mathsf{g(-3)\:.\:g(-2)\:.\:(g(-1) = (\sqrt{2})^{3}\:.\:(\sqrt{2})^{2}\:.\:(\sqrt{2})^{1}}$

$\mathsf{g(-3)\:.\:g(-2)\:.\:(g(-1) = (\sqrt{2})^{6}}$

$\boxed{\boxed{\mathsf{g(-3)\:.\:g(-2)\:.\:(g(-1) = 8}}}$