Let f be a function such that 24 f(x) 3f (24/x)= 4x, x ≠ 0. Then f(3) + f(8) is equal to

Question

Let f be a function such that \(f(x)+3 f\left(\frac{24}{x}\right)=4 x, x \neq 0.\) Then f(3) + f(8) is equal to

(1) 11

(2) 10

(3) 12

(4) 13 

Answer 1

Correct option is: (1) 11 

\(f(x)+3 f\left(\frac{24}{x}\right) = 4x\) 

put x = 3 

f(3) + 3f(8) = 12 … (1) 

put x = 8 

f(8) + 3f(8) = 32 … (2)

(1) + (2) 

\(4(f(3) + f(8)) = 44 \Rightarrow f(3) + f(8) = 11\)