TS ICET 2017 Question Paper with Solutions for online practice

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Question : 74 of 200

Marks: +1, -0

lf f{x) =

x^3

and g(x) =

3^x

for x > 0, then {x > 0 : f(g(x)) = g(f(x))} =

ϕ
{x : x > 0}
{0, $√3$ }
{ $√3$ }

Solution:

Given :

f(x)=x^3,g(x)=3^x

f(g(x))=f(3^x)=(3^x)^3=3^{3x}

...(i)

g(f(x))=g(x^3)=3^{x^3}

...(ii)
According to the question,

3^{x^3}=3^{3x}⇒x^3=3x⇒x^2=3⇒x=√3

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