First slide

Functions (XII)

Question

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

Moderate

A

8
B

4
C

-8
D

11

Solution

$\begin{array}{l} 3 f (x) + 2 f (\frac{x + 59}{x - 1}) = 10 x + 30 \\ For x = 7, 3 f (7) + 2 f (11) = 70 + 30 = 100 \\ For x = 11, 3 f (11) + 2 f (7) = 140 . \\ \frac{f (7)}{- 20} = \frac{f (11)}{- 220} = \frac{- 1}{9 - 4} or f (7) = 4 \end{array}$

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