Question

(MACK-02) Se x >1 e f (x) = x / (x – 1), então f(f(x + 1)) é igual a:

a) x + 1
b) 1 / (x – 1)
c) x – 1
d) x / (x – 1)
e) (x + 1) / (x – 1)

Answer 1

f(x)=x/x+1

substituindo em x, x+1

f(x+1)=x+1/(x+1-1)

f(x+1)=x+1/x

agora fazendo

f(f(x+1))=(x+1/x)/(x+1/x-1)

=x+1/x(x+1-x/x)

=x+1/x(1/x)

=x+1

$\boxed{ \boxed{ \boxed{ \mathsf{alternativa \: \huge{ \textbf{ \textit{(a).}}}}}}}$

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