If $2f(x + 1) + f\left( \frac{1}{x + 1} ight) = 2x$ and $x
eq - 1$, then $f(2)$ is equal to

Question

If $2f(x + 1) + f\left( \frac{1}{x + 1} ight) = 2x$ and $x 
eq - 1$, then $f(2)$ is equal to

Dr. Abubacker · Accepted Answer

(c)
Put, $x = 1,\  - \frac{1}{2}$ in given function respectively, we get
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2f(2) + f\left( \frac{1}{2} \right) = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
And $2f\left( \frac{1}{2} \right) + f(2) = - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
On solving Eqs. (i) and (ii), we get $f(2) = \frac{5}{3}$

Q. If $2f(x + 1) + f\left( \frac{1}{x + 1} \right) = 2x$ and $x \neq - 1$, then $f(2)$ is equal to

Explanation

Reviewed by Dr. Abubacker

Want more practice?