Question

x³ + 3/ x² - 1
Calcule: f(1/3) + f(- 1/2) =

Answer 1

Bom dia  Amanda!

Solução!

Vamos resolver cada item separado,no final fazemos a soma.

$f\left ( \dfrac{1}{3} \right )= \dfrac{ x^{3}+3 }{ x^{2} -1}\\\\\\\ f\left ( \dfrac{1}{3} \right )= \dfrac{ \left ( \dfrac{1}{3} \right )^{3}+3 }{ \left ( \dfrac{1}{3} \right )^{2} -1}\\\\\\\ f\left ( \dfrac{1}{3} \right )= \dfrac{ \left ( \dfrac{1}{27} \right )+3 }{ \left ( \dfrac{1}{9} \right ) -1}\\\\\\\ f\left ( \dfrac{1}{3} \right )= \dfrac{ \left ( \dfrac{1+81}{27} \right ) }{ \left ( \dfrac{1-9}{9} \right) }$

$f\left ( \dfrac{1}{3} \right )= \dfrac{ \left ( \dfrac{82}{27} \right ) }{ \left ( -\dfrac{8}{9} \right) }\\\\\\\ f\left ( \dfrac{1}{3} \right )=\left ( \dfrac{82}{27} \right )\times\left (- \dfrac{9}{8} \right )\\\\\\\\ f\left ( \dfrac{1}{3} \right )=\left ( \dfrac{41}{3} \right )\times\left (- \dfrac{1}{4} \right )\\\\\\\\ \boxed{f\left ( \dfrac{1}{3} \right )=\left (- \dfrac{41}{12} \right )}$


$f\left ( \dfrac{1}{2} \right )= \dfrac{ x^{3}+3 }{ x^{2} -1}\\\\\\\\ f\left ( \dfrac{1}{2} \right )= \dfrac{\left ( \dfrac{1}{2} \right ) ^{3}+3 }{\left ( \dfrac{1}{2} \right ) ^{2} -1}\\\\\\\ f\left ( \dfrac{1}{2} \right )= \dfrac{\left ( \dfrac{1}{8} \right ) +3 }{\left ( \dfrac{1}{4} \right ) -1}\\\\\\\ f\left ( \dfrac{1}{2} \right )= \dfrac{\left ( \dfrac{1+24}{8} \right ) }{\left ( \dfrac{1-4}{4} \right )}$



$f\left ( \dfrac{1}{2} \right )= \dfrac{\left ( \dfrac{25}{8} \right ) }{\left ( -\dfrac{3}{4} \right )}\\\\\\\ f\left ( \dfrac{1}{2} \right )=\left ( \dfrac{25}{8} \right ) \times\left ( -\dfrac{4}{3} \right )\\\\\\\\\ f\left ( \dfrac{1}{2} \right )=\left ( \dfrac{25}{2} \right ) \times\left ( -\dfrac{1}{3} \right )\\\\\\\\\ \boxed{f\left ( \dfrac{1}{2} \right )=- \dfrac{25}{6} }$



$f\left ( \dfrac{1}{3} \right )+f\left ( \dfrac{1}{2} \right )\\\\\\\ -\dfrac{41}{12}- \dfrac{25}{6} \\\\\\\\ \dfrac{-41-50}{12}\\\\\\\ \boxed{Resposta~~ -\dfrac{91}{12} }$



Bom dia!
Bons estudos!

Answer 2

Calcular f(1/3) signfica substituir o valor de x por 1/3, ou seja:
     f(1/3)=x³ + 3/x² - 1
=> f(1/3)=(1/3)³ + 3/(1/3)² - 1
=> f(1/3)=1/27 + (3/1)/(1/9) - 1 note que (3/1)=3 e que para resolver esta fração fazemos uma multiplicação ente o 3 e o 9 e o 1 e o 1 , pesquise por meio pelos extremos, ou "orelhinha orelhão", logo :
=> f(1/3)=1/27+27/1 - 1
=> f(1/3)=1/27+27²/27 - 1
=> f(1/3)=(1+27²)/27 - 1
=> f(1/3)=(1+729)/27 -1
=> f(1/3)=730/27 - 1
=> f(1/3)=730/27 - 27/27 (pois -27/27 = -1)
=> f(1/3)=(730-27)/27
=> f(1/3)=703/27=26,037...