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Grade 12th passIIT JEE Entrance Exam

F(x)=3x-1 and g(x)=x(x-1) then g(f^-1(x)) is ;??? a) (x/3)(x+1) b) (x/3)(x-1) c) 3x(3x-1) d) (x/3)(x/3 +1)

Profile image of Hamid Ali Shah
8 Years agoGrade 12th pass
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1 Answer

Profile image of Arun
8 Years ago

f(x)=y=3x-1

switching the variables to find the inverse function;

x=3y-1

y=(x+1)/3

thus f-¹(x)=(x+1)/3

g(f-¹(x))=f-¹(x)(f-¹(x)-1)

=((x+1)/3)*((x+1)/3)-1)

= ((x+1)/3)*((x+1–3)/3)

= ((x+1)(x-2))/9

= (x^2 - x - 2)/9

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