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If g be the inverse of function f, then  g(x)=f1(x)f(g(x))=xf|(g(x))g|(x)=1g|(x)=1f|(g(x)) also , if f(α)=β, then g(β)=α

From (1), g|(β)=1f|[g(β)]g|(β)=1f|(α), where  f(α)=β

If  f:RR defined by f(x)=x5+e2x and g is the inverse of f , then g|(1)=

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By Expert Faculty of Sri Chaitanya
a
2
b
1
c
12
d
none of these
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detailed solution

Correct option is C

f(x)=x5+e2x

f(0)=0+e0=1

f|(x)=5.x4+2.e2xf|(0)=5(0)+2(1)=2

(gof)(x)=xg[f(x)]=x

g|f(x).f|(x)=1

g|f(x)=1f|(x)

put  x=0

g|(f(0))=1f|(0)

g|(1)=12


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