JEE Main 2017 · 8 Apr · Shift 1 · Mathematics Q61

← JEE Main 2017 · 8 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 61 of 90

Let $f(x)=2^{10}\cdot x+1$ and $g(x)=3^{10}\cdot x-1$ . If $(f\circ g)(x)=x$ , then $x$ is equal to :

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

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

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

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

Answer and worked solution

Official answer: D

$f(g(x))=2^{10}(3^{10}x-1)+1=6^{10}x-2^{10}+1=x$ , so
$x=\frac{2^{10}-1}{6^{10}-1}=\frac{1-2^{-10}}{3^{10}-2^{-10}}$
(dividing top and bottom by $2^{10}$ ).

Topics:Composition and inverse functions

← Previous question Next question →

JEE Main 2017 · 8 Apr · Shift 1, Mathematics question 61