JEE Main 2025 Apr 3 Shift 2, Mathematics Q10: Introduction Of Functions

JEE Main2025Apr 3, Shift 2Mathematics

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

Solution

Note that $24/3 = 8$ and $24/8 = 3$ , so substituting $x = 3$ and $x = 8$ produces two linear equations in $f (3)$ and $f (8)$ .

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

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

Adding: $4 (f (3) + f (8)) = 44 \Rightarrow f (3) + f (8) = 11$ .

Concept behind this question

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