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Question
If f : R → R defined by f(x) = 3x − 4 is invertible, then write f−1 (x).
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Solution
\[Let f^{- 1} \left( x \right) = y . . . \left( 1 \right)\]
\[ \Rightarrow f\left( y \right) = x\]
\[ \Rightarrow 3y - 4 = x\]
\[ \Rightarrow 3y = x + 4\]
\[ \Rightarrow y = \frac{x + 4}{3}\]
\[ \Rightarrow f^{- 1} \left( x \right) = \frac{x + 4}{3} [from\left( 1 \right)]\]
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