Mathematics - Functions Question with Solution | TestHub

Given: $f\left(x\right)=\frac{4x+3}{6x-4}$

$\Rightarrow fof\left(x\right)=\frac{4\left(\frac{4x+3}{6x-4}\right)+3}{6\left(\frac{4x+3}{6x-4}\right)-4}$

$\Rightarrow fof\left(x\right)=\frac{16x+12+18x-12}{24x+18-24x+16}$

$\Rightarrow fof\left(x\right)=\frac{34x}{34}$

$\Rightarrow fof\left(x\right)=x$

$\Rightarrow g\left(x\right)=x$

$\Rightarrow gog\left(x\right)=x$

$\Rightarrow gogog\left(x\right)=x$

$\Rightarrow gogog\left(4\right)=4$