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Question
If f : R → R is defined by f(x) = 10 x − 7, then write f−1 (x).
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Solution
\[Let f^{- 1} \left( x \right) = y . . . \left( 1 \right)\]
\[ \Rightarrow f\left( y \right) = x\]
\[ \Rightarrow 10y - 7 = x\]
\[ \Rightarrow 10y = x + 7\]
\[ \Rightarrow y = \frac{x + 7}{10}\]
\[ \Rightarrow f^{- 1} \left( x \right) = \frac{x + 7}{10} \left( \text{ From}\left( 1 \right) \right)\]
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