Question

The function $f$ satisfies the functional equation
$3f\left(x\right)+2f\left(\frac{x+59}{x-1}\right)=10x+30$ for all real $x\ne 1$ The value of $f\left(7\right)$ is

Answer 1

Answer: 4

$3f\left(x\right)+2f\left(\frac{x+59}{x-1}\right)=10x+30$
For $x=7,3f\left(7\right)2f\left(11\right)=7030=100$
For $x=11,3f\left(11\right)+2f\left(7\right)=140$
$\frac{f\left(7\right)}{-20}=\frac{f\left(11\right)}{-220}=\frac{-1}{9-4}$
$\Rightarrow f\left(7\right)=4$