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

We are given $$f(x) + 3f\left(\dfrac{24}{x}\right) = 4x$$ for $$x \neq 0$$.

Substituting $$x = 3$$: $$f(3) + 3f(8) = 12$$ ... (i)

Substituting $$x = 8$$: $$f(8) + 3f(3) = 32$$ ... (ii)

Adding equations (i) and (ii): $$f(3) + 3f(8) + f(8) + 3f(3) = 12 + 32$$

$$4f(3) + 4f(8) = 44$$

$$f(3) + f(8) = 11$$

Hence, the correct answer is Option A.

Create a FREE account and get:

Predict your JEE Main percentile, rank & performance in seconds

Check Your Score Now

Ask our AI anything

AI can make mistakes. Please verify important information.

Download resources