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Question
If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]
Solution
Given: \[f\left( x \right) = 1 - \frac{1}{x}\]
Now, \[f\left( \frac{1}{x} \right) = 1 - \frac{1}{\frac{1}{x}} = 1 - x\]
If \[f\left( x \right) = 1 - \frac{1}{x}\]
\[ = \frac{- x}{1 - x}\]
\[ = \frac{- x}{- \left( x - 1 \right)}\]
\[ = \frac{x}{x - 1}\]
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