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Most Important Selected Qs for JEE AdvancedMathematicsDifferentiation

Let f: R R be a function defined by f(x)=x^3+2 x^2+3 x+2 and g be the inverse function of f . If . d d x (g(g(g(x)))) |_ x=24 = p q , where p, q are co-prime, then find the value of (p+q) .

Correct answer

139

Step-by-step solution

aligned & 9) f(-1)=0, f(0)=2 and f(2)=24, f^ (x)=3 x^2+4 x+3 & d d x (g(g(g(x))))=g^ (g(g(x))) g^ (g(x)) g^ (x) & . d d x (g(g(g(x)))) |_ x=24 =g^ (g(g(24))) g^ (g(24)) g^ (24)=g^ (g(2)) g^ (2) 1 f^ (2) & =g^ (0) 1 f^ (0) 1 f^ (2) = 1 f^ (-1) 1 f^ (0) 1 f^ (2) = 1 2 1 3 1 23 = 1 138 p q & p p=139 aligned

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