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  4. The function f satisfies the functional equation 3f(x)+2f((x +59/x-1)) =10x +30 for all real x≠1 The value of f(7) is

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Q. The function $f$ satisfies the functional equation
$3f\left(x\right)+2f\left(\frac{x +59}{x-1}\right) =10x +30$ for all real $x\ne1$ The value of $f\left(7\right)$ is

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Solution:

$3f\left(x\right)+2f\left(\frac{x +59}{x-1}\right) =10x +30$
For $x =7, 3f\left(7\right) 2f\left(11\right) =70 30 =100$
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 $