Question

considerando a função f(x)=x+1/x, calcule:

F(5)=
F(F(5)=

​

Answer 1

Para determinarmos o valor de f(5), basta substituirmos o "x" da função por 5 e, sendo assim, temos:

$f(x)~=~x~+~\dfrac{1}{x}\\\\\\f(5)~=~5~+~\dfrac{1}{5}~~~\rightarrow~MMC=5\\\\\\f(5)~=~\dfrac{5\cdot5~+~1\cdot1}{5}\\\\\\f(5)~=~\dfrac{25~+~1}{5}\\\\\\\boxed{f(5)~=~\dfrac{26}{5}}$

Com o valor de calculado de f(5), podemos calcular o resultado da função composta f(f(x)) para x=5, ou seja, f(f(5)):

$f(f(5))~=~f\left(\dfrac{26}{5}\right)\\\\\\f(f(5))~=~\dfrac{26}{5}~+~\dfrac{1}{\dfrac{26}{5}}\\\\\\f(f(5))~=~\dfrac{26}{5}~+~\dfrac{1}{1}\cdot\dfrac{5}{26}\\\\\\f(f(5))~=~\dfrac{26}{5}~+~\dfrac{5}{26}~~~\rightarrow~MMC=5\cdot26=130\\\\\\f(f(5))~=~\dfrac{26\cdot26~+~5\cdot5}{5\cdot26}\\\\\\f(f(5))~=~\dfrac{676~+~25}{130}\\\\\\\boxed{f(f(5))~=~\dfrac{701}{130}}$