If $$ f(x)=1-\frac{1}{x} $$, then $$ (f \circ f)\left(\frac{1}{x}\right)= $$

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To find $$ (f \circ f)\left(\frac{1}{x}\right) $$, we need to first find $$ f\left(\frac{1}{x}\right) $$ and then substitute this value into the function $$ f(x) $$ to get the final result.

Given that $$ f(x) = 1 - \frac{1}{x} $$, let's first find $$ f\left(\frac{1}{x}\right) $$:

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

Now, we substitute $$ f\left(\frac{1}{x}\right) = 1 - x $$ into the function $$ f(x) $$ to find $$ (f \circ f)\left(\frac{1}{x}\right) $$:

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

Therefore, $$ (f \circ f)\left(\frac{1}{x}\right) = 1 - \frac{1}{1 - x} $$.
$$ (f \circ f)\left(\frac{1}{x}\right) = 1 - \frac{1}{1 - x} $$

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