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Question

Let f:RR be a function defined by f(x)=x3+x2+x1. If g is the inverse of f, then g(2) is

A
2
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B
6
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C
16
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D
12
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Solution

The correct option is C 16
We have, g(x)=f1(x)f(g(x))=x
Differentiating both sides w.r.t. x, we get
f(g(x))×g(x)=1
f(x)=3x2+2x+1

Let g(2)=K
We know f(g(2))=2
f(K)=2
K3+K2+K1=2
K3+K2+K3=0
K=1g(2)=1.
g(x)=1f(g(x))
g(2)=1f(g(2))=1f(1)=16 (f(1)=6)

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