Question

If f(x) is a positive integer function.f(x)/f(x-1)=(x-2)/(x+1) for all x>=0 f(6)=81 and f(2)=4 then find f(4)

Answer 1

Answer:

$\frac{2}{5}$

Step-by-step explanation:

Given,

$\frac{f(x)}{f(x-1)}=\frac{x-2}{x+1}$

Where, x ≥ 0,

If x = 3,

$\frac{f(3)}{f(2)}=\frac{3-2}{3+1}=\frac{1}{4}$

We have, f(2) = 4,

$\frac{f(3)}{4}=\frac{1}{4}$

$\implies f(3) = 1$

If x = 4,

$\frac{f(4)}{f(3)}=\frac{4-2}{4+1}=\frac{2}{5}$

$\frac{f(4)}{1}=\frac{2}{5}$

$\implies f(4)=\frac{2}{5}$