The function f satisfies the functional equation 3f(x) + 2f ( x +… - Vidyadip

MCQ

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

A
$8$
✓
$4$
C
$-8$
D
$11$

✓

Answer

Correct option: B.

$4$

b
(b) $3f(x) + 2f\left( {\frac{{x + 59}}{{x - 1}}} \right) = 10x + 30$

For $x = 7$, $3f(7) + 2f(11) = 70 + 30 = 100$

For $x = 11$, $3f(11) + 2f(7) = 140$

$\frac{{f(7)}}{{ - 20}} = \frac{{f(11)}}{{ - 220}} = \frac{{ - 1}}{{9 - 4}}$ ==> $f(7) = 4$.

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