Question

Considere f(x) = \frac{1}{x-1}  . O valor de x, de modo que fof(x) = 1, é:

a) 1.$\frac{1}{x-1}$
b) 2.$\frac{1}{x-1}$
c) 1,5.
d) 2,5.
e) –1.

Answer 1

$f(x)= \frac{1}{x-1} \\ \\f(fx)=\frac{1}{\frac{1}{x-1} -1}= \frac{1}{\frac{1}{x-1}-\frac{x-1}{x-1}} = \frac{1}{ \frac{1-x+1}{x-1}}= \frac{1}{ \frac{-x+2}{x-1}} = \frac{x-1}{2-x} \\ \\f(f(x)=1, \ logo: \\\ \frac{x-1}{2-x}=1\\ x-1=2-x\\ x+x=2+1\\ 2x=3\\ x= \frac{3}{2}$

Answer 2

Boa tarde!

Solução!

$fof(x)=1\\\\\\ \dfrac{1}{x-1}=1\\\\\\\ \dfrac{1}{ \dfrac{1}{x-1} -1}=1\\\\\\ \dfrac{1}{ \dfrac{1-x+1}{x-1} }=1\\\\\\ \dfrac{1}{ \dfrac{2-x}{x-1} }=1\\\\\\ \dfrac{x-1}{2-x}=1 \\\\\ x-1=2-x\\\\\ x+x=2+1\\\\\\ 2x=3\\\\\ x= \dfrac{3}{2}\\\\\\ x=1,5$

Resposta: Alternativa C

Boa tarde!
Bons estudos!