Question

function answer these​

Answer 1

Step-by-step explanation:

We have,

$f(x) = 1 + \dfrac{1}{x - 1}$

$\implies \: f(x) = \dfrac{x - 1 + 1}{x - 1}$

$\implies \: f(x) = \dfrac{x }{x - 1}$

Here, x ≠ 1,

Now,

$\implies \: f(f(x)) = \dfrac{f(x)}{f(x) - 1}$

$\implies \: f(f(x)) = \dfrac{ \dfrac{x}{x - 1} }{ \dfrac{x}{x - 1} - 1}$

$\implies \: f(f(x)) = \dfrac{ \dfrac{x}{x - 1} }{ \dfrac{x - x + 1}{x - 1} }$

$\implies \: f(f(x)) = \dfrac{ x }{x - x + 1 }$

$\implies \: f(f(x)) = x$

Now,

$\implies \: f(f(x)) = f(x)$

$\implies \: x= \dfrac{x}{x - 1}$

$\implies \: x^{2} - x= x$

$\implies \: x^{2} - 2x= 0$

$\implies \: x(x - 2)= 0$

$\implies \: x = 0 \: \: \: \: or \: \: \: \: x = 2$