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Question
Let f : R → R+ be defined by f(x) = ax, a > 0 and a ≠ 1. Write f−1 (x).
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Solution
\[Let f^{- 1} \left( x \right) = y . . . \left( 1 \right)\]
\[ \Rightarrow f\left( y \right) = x\]
\[ \Rightarrow a^y = x\]
\[ \Rightarrow y = \log_a x\]
\[ \Rightarrow f^{- 1} \left( x \right) = \log {}_a x [ \text{from }\left( 1 \right)]\]
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