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Question
If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).
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Solution
\[ = f \left( \left( 3 - x^3 \right)^\frac{1}{3} \right)\]
\[ = \left[ 3 - \left( \left( 3 - x^3 \right)^\frac{1}{3} \right)^3 \right]^\frac{1}{3} \]
\[ = \left[ 3 - \left( 3 - x^3 \right) \right]^\frac{1}{3} \]
\[ = \left( x^3 \right)^\frac{1}{3} \]
\[ = x\]
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