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Ex 1.3, 13 - f(x) = (3 - x3)1/3, then fof (x) is (A) x1/3 - Ex 1.3

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  1. Class 12
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Ex1.3 , 13 If f: R → R be given by f(x) = ﷐(3 – x3)﷮﷐1﷮3﷯﷯ , then fof(x) is (A) ﷐x﷮﷐1﷮3﷯﷯ (B) x3 (C) x (D) (3 – x3) f(x) = ﷐(3 – x3)﷮﷐1﷮3﷯﷯ f(f(x)) = ﷐(3 – f(x)3)﷮﷐1﷮3﷯﷯ fof(x) = ﷐﷐3 – ﷐﷐﷐(3 – x3)﷮﷐1﷮3﷯﷯﷯﷮3﷯﷯﷮﷐1﷮3﷯﷯ = ﷐﷐3 – ﷐(3 – x3)﷮﷐1﷮3﷯ × 3﷯﷯﷮﷐1﷮3﷯﷯ = ﷐﷐3 – ﷐(3 – x3)﷮1﷯﷯﷮﷐1﷮3﷯﷯ = ﷐﷐3 – 3 + x3﷯﷮﷐1﷮3﷯﷯ = ﷐﷐x3﷯﷮﷐1﷮3﷯﷯ = x Hence fof(x) = x So, C is the correct answer

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