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  4. If f (x)=(3x+2/5x-3), then (fof)(x) is

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

Relations and Functions - Part 2

Solution:

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