# If f(x)

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,

$f(1-x)=1-\frac{1}{1-x}$

$=\frac{1-x-1}{1-x}$

$=\frac{-x}{1-x}$

$=\frac{-x}{-(x-1)}$

$=\frac{x}{x-1}$