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If f : R → R be given by f (x) = (3 − x) to the power 3 the whole power 1 over 3, then fof (x) is A x to the power 1 over 3 B x to the power 3 C x D 3 - x to the power 3

Q.  13 If f : R \rightarrow R be given by f(x) = (3 - x^3)^{\frac{1}{3}}, then fof(x) is 

(A) x^{\frac{1}{3}}

(B) x^3

(C) x

(D) (3 - x^3)

Answers (1)
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f(x) = (3 - x^3)^{\frac{1}{3}}

fof(x)=f(f(x))=f((3-x^{3})^{\frac{1}{3}})

                                     =[3- ((3-x^{3})^{\frac{1}{3}})^{3}]^{\frac{1}{3}}

                                =([3- ((3-x^{3})]^{\frac{1}{3}})

                                   = (x^{3})^{\frac{1}{3}}

                                   =x

Thus,fof(x) is x.

Hence, option c is correct answer.

 

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