Mark (√) against the correct answer in the following:If f(x)\(=\sqrt

1.	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
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

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

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