Question

If $f(x)=\frac{2x+3}{3x-2}$, prove that fof is identity function.

Answer 1

any function is said to be identity function that always returns the same value that was used as its argument. mathematically, identity function is written as f(x) = x.

now, f(x) = (2x + 3)/(3x - 2)

fof = f(f(x)) = f[(2x + 3)/(3x - 2)]

= {2(2x + 3)/(3x - 2) + 3}/{3(2x + 3)/(3x - 2) - 2}

= {2(2x + 3) + 3(3x - 2)}/{3(2x + 3) -2(3x - 2)}

= {4x + 6 + 9x - 6}/{6x + 9 - 6x + 4}

= 13x/13

= x

hence, fof = x

it is clear that, fof is an identity function.