Functions Question 674
Question: The function f satisfies the functional equation $ 3f(x)+2f( \frac{x+59}{x-1} )=10x+30 $ for all real $ x\ne 1 $ . The value of $ f(7) $ is
[Kerala (Engg.) 2005]
Options:
A) 8
B) 4
C) ?8
D) 11
E) 44
Show Answer
Answer:
Correct Answer: B
Solution:
$ 3f(x)+2f( \frac{x+59}{x-1} )=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} $
Þ $ f(7)=4 $ .
BETA
