Let f be a function such that f(x)+3f((24)/(x))=4x,x 0.

Question

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

Accepted Answer

$\begin{gathered} f(x)+3f(\frac{24}{x})=4x,x
e 0\, \ldots (1) \ x\frac{24}{x} \ f(\frac{24}{x})+3f(\frac{24}{24})=4(\frac{24}{x})=\frac{96}{x}\, \ldots (2) \ 3	imes (2)-(1) \ \Rightarrow 8f(x)=\frac{96.3}{x}-4x\Rightarrow f(x)=\frac{36}{x}-\frac{x}{2} \ f(3)+f(8)=(12-\frac{3}{2})+(\frac{36}{8}-4) \end{gathered}$

$=8+\frac{36}{8}-\frac{12}{8}=11$

Solutions · 1