Mathematics | MHT CET 2020 | Discussion Page

If $f(x)=\frac{2x+3}{3x-2},x\neq\frac{2}{3}$ , then the function f of is

A) a constant function

B) an exponential function

C) an even function

D) an identity function

Option D

we have,

$f(x)=\frac{2x+3}{3x-2}$

$fof=f(f(x))=\frac{2f(x)+3}{3f(x)-2}$

$\Rightarrow fof=\frac{2(\frac{2x+3}{3x-2})+3}{3(\frac{2x+3}{3x-2})-2}$

$\Rightarrow$ $fof=\frac{4x+6+9x-6}{6x+9-6x+4}$

$\Rightarrow fof=\frac{13x}{13}=x=$ an identity function.

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