f(2x−5) + f(3x+5) = 7x−16 f(x) = ?


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Question Number 59942 by naka3546 last updated on 16/May/19

$f (2 x - 5) + f (3 x + 5) = 7 x - 16$ $f (x) = ?$
	Answered by mr W last updated on 16/May/19

	$l e t f (x) = a x + b$ $f (2 x - 5) + f (3 x + 5) = a (2 x - 5) + b + a (3 x + 5) + b$ $= 5 a x + 2 b$ $= 7 x - 16$ $\Rightarrow 5 a = 7 \Rightarrow a = \frac{7}{5}$ $\Rightarrow 2 b = - 16 \Rightarrow b = - 8$ $\Rightarrow f (x) = \frac{7}{5} x - 8$
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