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  4. If 2f(x +1) +f((1/x +1)) = 2x,then f (2) is equal to

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

Relations and Functions

Solution:

$2f\left(x +1\right) +f\left(\frac{1}{x +1}\right) = 2x ....\left(i\right)$
at $x =1$
$2f\left(2\right) +f\left(\frac{1}{2}\right) = 2 .....\left(ii\right)$
from equation (i)
Putting $x = -1/2$
$\Rightarrow 2f\left(\frac{1}{2}\right) + f\left(2\right) = -1 ....\left(iii\right)$
from equation (ii) and equation (iii)
$f\left(2\right) =5/3 =1.67$