Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • 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

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

In JEE Main 2025 April 3 shift 2, chemistry takes U-turn to be tougher than physics, mathematics
anam-khan

JEE Main 2025 April 3 Exam Analysis 2025: Shift 1 paper easy to moderate; chemistry section ‘easiest’
anam-khan

JEE Mains 2025 admit card out for April 7, 8, 9 exams; download on jeemain.nta.nic.in

Latest Question