Question:
If $f(x)=1-\frac{1}{x}$, then write the value of $f\left(f\left(\frac{1}{x}\right)\right)$.
Solution:
Given:
$f(x)=1-\frac{1}{x}$
Now,
$f\left(\frac{1}{x}\right)=1-\frac{1}{\frac{1}{x}}=1-x$
$\Rightarrow f\left(f\left(\frac{1}{x}\right)\right)=f(1-x)$
Again,
If $f(x)=1-\frac{1}{x}$
Thus,
$f(1-x)=1-\frac{1}{1-x}$
$=\frac{1-x-1}{1-x}$
$=\frac{-x}{1-x}$
$=\frac{-x}{-(x-1)}$
$=\frac{x}{x-1}$