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Question
If f(x) = 4 −( x - 7)3 then write f-1 (x).
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Solution
\[\text{We have}, \]
\[f\left( x \right) = 4 - \left( x - 7 \right)^3 \]
\[\text{Let y} = 4 - \left( x - 7 \right)^3 \]
\[ \Rightarrow \left( x - 7 \right)^3 = 4 - y\]
\[ \Rightarrow x - 7 = \sqrt[3]{4 - y}\]
\[ \Rightarrow x = 7 + \sqrt[3]{4 - y}\]
\[ \Rightarrow f^{- 1} \left( y \right) = 7 + \sqrt[3]{4 - y}\]
\[ \therefore f^{- 1} \left( x \right) = 7 + \sqrt[3]{4 - x}\]
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