Mathematics - Functions Question with Solution | TestHub

Given $f\left(g\left(x\right)\right)=x$

Where,$f\left(x\right)=2^{10}x+1$ ,$g\left(x\right)=3^{10}x-1.$

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

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

$\Rightarrow x\left(6^{10}-1\right)=2^{10}-1$

$\Rightarrow x=\frac{2^{10}-1}{6^{10}-1}=\frac{{\displaystyle \frac{2^{10}-1}{2^{10}}}}{{\displaystyle \frac{(2\times 3{)}^{10}-1}{2^{10}}}}$

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