Question

Seja f: R* → R a função dada por f(x) = (x²+1)/x, Qual é o valor de f(3) + f(1/3)?

20/3

1/3

10/3

5/3

4/3

​

Answer 1

Explicação passo-a-passo:

=> f(3)

$\sf f(x)=\dfrac{x^2+1}{x}$

$\sf f(3)=\dfrac{3^2+1}{3}$

$\sf f(3)=\dfrac{9+1}{3}$

$\sf f(3)=\dfrac{10}{3}$

=> f(1/3)

$\sf f(x)=\dfrac{x^2+1}{x}$

$\sf f\Big(\dfrac{1}{3}\Big)=\dfrac{\Big(\frac{1}{3}\Big)^2+1}{\frac{1}{3}}$

$\sf f\Big(\dfrac{1}{3}\Big)=\dfrac{\frac{1}{9}+1}{\frac{1}{3}}$

$\sf f\Big(\dfrac{1}{3}\Big)=\dfrac{\frac{1+9}{9}}{\frac{1}{3}}$

$\sf f\Big(\dfrac{1}{3}\Big)=\dfrac{\frac{10}{9}}{\frac{1}{3}}$

$\sf f\Big(\dfrac{1}{3}\Big)=\dfrac{10}{9}\cdot\dfrac{3}{1}$

$\sf f\Big(\dfrac{1}{3}\Big)=\dfrac{30}{9}$

$\sf f\Big(\dfrac{1}{3}\Big)=\dfrac{10}{3}$

Assim:

$\sf f(3)+f\Big(\dfrac{1}{3}\Big)=\dfrac{10}{3}+\dfrac{10}{3}$

$\sf f(3)+f\Big(\dfrac{1}{3}\Big)=\dfrac{10+10}{3}$

$\sf \red{f(3)+f\Big(\dfrac{1}{3}\Big)=\dfrac{20}{3}}$

=> 20/3