Given that f(x) = x×f(x - 1) for any natural number x. If f(x + 2) = 20*f(x), then what is the value of x?
Choose the correct option
A) 5  B) 6  C) 7  D) 8  E) 98
Given:f(x) = x××f(x - 1) ....(a)   and f(x + 2) = 20××f(x) ....(b)   Substitute x = x + 1 in (a)   Then, f(x + 1) = (x + 1)××f(x) .........(c)   Substitute x = x + 2 in (a)   Then, f(x + 2) = (x + 2)××f(x + 1) ......(d)   From (b), 20××f(x) = f(x + 2) = (x + 2)××f(x + 1)= (x + 2)(x + 1)××f(x)   ⇒⇒ 20××f(x) = (x + 2) (x + 1)××(f(x)   Cancelling f(x) on both sides and upon simplification we get   or x2x2+ 3x - 18 = 0   or (x + 6)(x - 3) = 0   or x = -6 or 3. Hence the answer is option (e).   Answer:6
<result>B</result>
Given that f(x) = x×f(x - 1) for any natural number x. If f(x + 2) = 20*f(x), then what is the value of x?