Let f be a function such that $3f(x) + 2f\left( \frac{m}{19x} ight) = 5x$, $x
eq 0$, where $m =

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Let f be a function such that $3f(x) + 2f\left( \frac{m}{19x} ight) = 5x$, $x 
eq 0$, where $m = \sum_{i = 1}^{9}\mspace{2mu}(i)^{2}$. Then $f(5) - f(2)$ is equal to

Accepted Answer

$m = \frac{9 	imes 10 	imes 19}{6} = 15 	imes 19$$$3f(x) + 2f\left( \frac{15}{x} ight) = 5x $$Replace x by $\frac{15}{x}$$${3f\left( \frac{15}{x} ight) + 2f(x) = \frac{75}{x} }{9f(x) - 4f(x) = 15x - \frac{150}{x} }{5f(x) = 15x - \frac{150}{x} }{f(x) = 3x - \frac{30}{x} }{f(5) = 15 - \frac{30}{5} = 9 }{f(2) = 6 - 15 = - 9 }{f(5) - f(2) = 18}$$

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