Question

If $f\left(x\right)=\frac{2x+3}{3x-2}$
Prove that $fof$ is an identity function

Answer 1

$\begin{array}{c}f\left(x\right)=\frac{2x+3}{3x-2}\\ f\circ f\left(x\right)=f\left(f\left(x\right)\right)=f\left(\frac{2x+3}{3x-2}\right)\\ =\frac{2\left(\frac{2x+3}{3x-2}\right)+3}{3\left(\frac{2x+3}{3x-2}\right)-2}\\ =\frac{2x+6+9x-6}{6x+9-6x+4}\\ =\frac{13x}{13}\\ =x\\ f\circ f\left(x\right)=x\end{array}$

$f\circ f$ is an identity function