Value of f(x)

Q.24: If $\frac{f(x)}{f(x-1)} = \frac{(x-2)}{(x+1)}$, for all x ≥ 0 and f(x) is a positive-valued function and f(6) = 81, f(2) = 4, find the value of f(4).

1. 8
2. 18
3. 25
4. 28

Detailed Solution

Taking x = 5,
$\frac{f(5)}{f(4)} = \frac{(3)}{(6)}$ ……………(1)
Taking x = 4,
$\frac{f(4)}{f(3)} = \frac{(2)}{(5)}$
=) f(5) = f(2) * $\frac{(3)}{(4)}$
Putting f(5) in equation (1),
We get (f(4))² = f(2)f(6) = 81 x 4
f(4) = 9 x 2 = 18
Answer choice (B).


Correct Answer: 18

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