Trail and Error!

Algebra Level pending

For a function $f(x)$ ,

$f(1) - f(-1) = 6\\f(2) - f(-2) = 3\\f(3) - f(-3) = 2\\f(6) - f(-6) = 1$

If the above information holds true, and $f(x) - f(-x)$ follows same pattern for all values of $x$ , find the value of $f(12) - f(-12)$

\frac{1}{2}

\frac{6}{5}

6

2

\frac{3}{7}

2 solutions

Viki Zeta
May 30, 2016

Seeing all those given information,

$f(1) - f(-1) = 6\\f(2) - f(-2) = 3\\f(3) - f(-3) = 2\\f(6) - f(-6) = 1$

It's clear that,

$f(x) - f(-x) = \frac{6}{x}$

So, $f(12) - f(-12) = \frac{6}{12} = \frac{1}{2}$

Santo Chandra
May 29, 2016

It's geometric series