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in Sets, Relations and Functions by (27.7k points)
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Mark (√) against the correct answer in the following:

If f(x)\(=\sqrt[3]{3-x^3}\) then (f o f) (x) = ?

\(A. x^{1/3}\)

\(B.x\)

\(C.(1-x^{1/3})\)

D . None of these

1 Answer

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by (25.7k points)
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Best answer

Correct Answer is (C) x

\(f(x)=\sqrt[3]{3-x^3}\)

\(\Rightarrow f(f(x))=\sqrt[3]{3-f(x)^3}\)\(=\sqrt[3]{3-(\sqrt[3]{3-x^3})^3}\)

\(\Rightarrow f(f(x))=\sqrt[3]{3-(3-x^3)}\)

\(\Rightarrow f(f(x))=\sqrt[3]{x^3}\) = x

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