JEE Main On 8 April 2017 Question 10
Question: Let $ f(x)=2^{10}dx+1 $ and $ g(x)=3^{10}x-1. $ If $ (fog)(x)=x, $ then x is equal to: [JEE Online 08-04-2017]
Options:
A) $ \frac{2^{10}-1}{2^{10}-{3^{-10}}} $
B) $ \frac{1-{2^{-10}}}{3^{10}-{2^{-10}}} $
C) $ \frac{3^{10}-1}{3^{10}-{2^{-10}}} $
D) $ \frac{1-{3^{-10}}}{2^{10}-{3^{-10}}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(g(x))=x $
$ f(3^{10}x-1)=2^{10}(3^{10}.x-1)=x $
$ =\frac{1}{3^{10}-{2^{-110}}} $
$ 2^{10}(3^{10}x-1)+1=x $
$ x(6^{10}-1)=2^{10}-1 $
$ x=\frac{2^{10}-1}{6^{10}-1}=\frac{1-{2^{-10}}}{3^{10}-{2^{-10}}} $
