JEE Main20245 Apr 2024Morning ShiftMathematicsFunctionsActual

Let f(x)=x^5+2 x^3+3 x+1, x R , and g(x) be a function such that g(f(x))=x for all x R . Then g(7) g^ (7) is equal to :

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Correct answer

A. 14

Step-by-step solution

aligned & f(x)=x^5+2 x^3+3 x+1 & f^ (x)=5 x^4+6 x^2+3 & f^ (1)=5+6+3=14 & g(f(x))=x & g^ (f(x)) f^ (x)=1 & for f(x)=7 & x^5+2 x^3+3 x+1=7 & x=1 & g^ (7) f^ (1)=1 g^ (7)= 1 f^ (1) = 1 14 aligned aligned & x=1, f(x)=7 g(7)=1 & g(7) g^ (7) = 1 1 / 14 =14 aligned

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