Question

If $f\left(x\right)=\frac{3x+2}{5x-3}$, then $(fof)(x)$ is

• A. $x$
• B. $-x$
• C. $f(x)$
• D. $-f(x)$

Answer 1

Answer: (A)

$\left(fof\right)\left(x\right)=f\left(f\left(x\right)\right)$
$=f\left(\frac{3x+2}{5x-3}\right)$
$=\frac{3\left(\frac{3x+2}{5x-3}\right)+2}{5\left(\frac{3x+2}{5x-2}\right)-2}$
$=\frac{9x+6+10x-6}{15x+10-15x+9}$
$=\frac{19x}{19}$
$=x$