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Question
If \[f : R \to R\] is given by \[f\left( x \right) = x^3 + 3, \text{then} f^{- 1} \left( x \right)\] is equal to
Options
\[x^{1/3} - 3\]
\[x^{1/3} + 3\]
\[\left( x - 3 \right)^{1/3}\]
\[x + 3^{1/3}\]
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Solution
(c) \[\text{Let} f^{- 1} \left( x \right) = y\]
\[f\left( y \right) = x\]
\[ \Rightarrow y^3 + 3 = x\]
\[ \Rightarrow y^3 = x - 3\]
\[ \Rightarrow y = \sqrt[3]{x - 3} \]
\[ \Rightarrow y = \left( x - 3 \right)^\frac{1}{3} \]
So, the answer is (c).
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