Question

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
• B. 4
• C. $ -8 $
• D. 11
• E. 44

Answer 1

Answer: (B)

Given that $ 3f(x)+2f\left( \frac{x+59}{x-1} \right)=10x+30 $ ...(i)
and < $ 3f\left( \frac{x+59}{x-1} \right)+2f(x)=\frac{40x+560}{x-1} $ ...(ii)
On solving Eqs. (i) and (ii), we get
$ f(x)=\frac{6{{x}^{2}}-4x-242}{x-1} $
$ \therefore $ $ f(7)=\frac{6\times 49-28-242}{6}=\frac{294-270}{6} $
$ =\frac{24}{6}=4 $