First slide

Algebra of real valued functions

Question

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

Moderate

A

8
B

4
C

-8
D

11

Solution

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

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App