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  • Try this! Let f (x)=210⋅x+1 and g(x)=310⋅x−1. If (fog)(x)=x, then x is equal to :

Let f (x)=210⋅x+1 and g(x)=310⋅x−1.  If (fog)(x)=x, then x is equal to :

 

  • Option 1) (310-1)/(310-2-10)

     

  • Option 2) (210-1)/(210-3-10)

     

  • Option 3) (1-3-10)/(210-3-10​​​​​​​)

     

  • Option 4) (1-210)/(310-2-10​​​​​​​)

     

 

Answers (1)

best_answer

Using 

f\left ( x \right )= 2^{10}x+1

g\left ( x \right )= 3^{10}x-1

Then, fog\left ( x \right )= f\left ( g\left ( x \right ) \right )

\Rightarrow f\left ( 3^{10}x-1 \right )= 2^{10}\left ( 3^{10}x-1 \right )+1= x

\Rightarrow 2^{10}\cdot 3^{10}x-2^{10}+1= x

\therefore 2^{10}\cdot 3^{10}x- x= 2^{10}-1

\therefore x\left ( 2^{10}\cdot 3^{10}-1 \right )= 2^{10}-1

\therefore x= \frac{2^{10}-1}{2^{10}\cdot 3^{10}-1}

\therefore x= \frac{1-2^{-10}}{3^{10}-2^{-10}}


Option 1)

\frac{3^{^{10}}-1}{3^{10}-2^{-10}}

Option 2)

\frac{2^{10}-1}{2^{10}-3^{-10}}

Option 3)

\frac{1-3^{-10}}{2^{10}-3^{-10}}

Option 4)

\frac{1-2^{-10}}{3^{10}-2^{-10}}

Posted by

Himanshu

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