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
$f(x)=\frac{6x^2-4x-242}{x-1}$
$\therefore$ $f(7)=\frac{6\times 49-28-242}{6}=\frac{294-270}{6}$
$=\frac{24}{6}=4$