Question

If $f\left(x\right)=\frac{x+1}{x-1}(x\ne \pm 1)$ then find
i) (fofof)(x)
ii) (fofofof)(x)

Answer 1

$f\left(x\right)=\frac{x+1}{x-1}$

$fof\left(x\right)=\frac{f\left(x\right)+1}{f\left(x\right)-1}=\frac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}=\frac{x+1+x-1}{x+1-x+1}=x$

$i\left)\right(fofof\left)\right(x)=f\left(fof\right(x\left)\right)=f\left(x\right)=\frac{x+1}{x-1}$

$ii\left)\right(fofofof\left)\right(x)=fof\left(fof\right(x\left)\right)=fof\left(x\right)=x$