Question ID: #1171
Let $f$ be a function such that $f(x)+3f\left(\frac{24}{x}\right)=4x$, $x\neq 0$. Then $f(3)+f(8)$ is equal to
- (1) 11
- (2) 10
- (3) 12
- (4) 13
Solution:
$$f(x)+3f\left(\frac{24}{x}\right)=4x$$
$$x = 3$$
$$f(3)+3f\left(\frac{24}{3}\right)=4(3)$$
$$f(3)+3f(8)=12$$
$$x = 8$$
$$f(8)+3f\left(\frac{24}{8}\right)=4(8)$$
$$f(8)+3f(3)=32$$
$$f(3) + 3f(8) + f(8) + 3f(3) = 12 + 32$$
$$4f(3) + 4f(8) = 44$$
$$4(f(3) + f(8)) = 44$$
$$f(3) + f(8) = 11$$
Ans. (1)
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