Discussion Forum



1)

 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

Answer:

Option D

Explanation:

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.