Question

if f(x)= 2x+3/3x-2. prove that fof is an identity function

Answer 1

We have to do this First,,.

Answer 2

Solution:

Yes, fof for the given function is an identity function. The proof is shown below in explanation.

Explanation:

We have been given that

$f(x)=\frac{2x+3}{y3x-2}$

Let us find the composite function fof and see if the result is an identity function or not.

$fof=f(f(x))\\\\==\frac{2\cdot \frac{2x+3}{3x-2}+3}{3\cdot \frac{2x+3}{3x-2}-2}\\\\=\frac{\frac{4x+6}{3x-2}+3}{\frac{6x+9}{3x-2}-2}\\\\=\frac{4x+6+9x-6}{6x+9-6x+4}\\\\=\frac{13x}{13}\\\\=x$

We can see that we got the result "x" which is an identity function.

Therefore, we can say that the composite function fof for the given function is an identity function.