Let y=f(x)(f: R \to R) be an explicit function defined by the implicit equation x^{3}+y^{3}+3(x^{2}+y^{2})+3(x+y)=14 and g be the inverse of f. If f \frac{d}{d x}(f(x+g(x)) \cdot g(x+f(x))) at x=-1+\sqrt[3]{15} is equal \lambda(15)^{2 \/ 3}, where \lambda \in I, then find the value of |\lambda| :

JEE Advanced 2020 Concept Recapitulation Test 4 Paper 2

Question : 51 of 54

Marks: +1, -0

Let y=f(x)(f:R→R) be an explicit function defined by the implicit equation x3+y3+3(x2+y2)+3(x+y)=14 and g be the inverse of f. If f‌

(f(x+g(x))⋅g(x+f(x))) at x=−1+√[3]15 is equal λ(15)2∕3, where λ∈I, then find the value of |λ| :

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