Question
Let f be a function such that 3 f(x)+2 f ( m 19 x )=5 x, x 0, where m= _ i=1 ^ 9 (i)^ 2 . Then f(5)-f(2) is equal to
JEE Main
Mathematics
Functions
2026
JEE Main 2026 (24 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 18
- B. 36
- C. 9
- D. -9
Answer
A. 18
Step-by-step solution
m = _ i=1 ^ 9 i^2 = 9 10 19 6 = 285, so m 19 = 15. The equation becomes 3f(x) + 2f ( 15 x ) = 5x ...(i) Replace x by 15 x : 3f ( 15 x ) + 2f(x) = 75 x ...(ii) From 3 (i) - 2 (ii): 5f(x) = 15x - 150 x , so f(x) = 3x - 30 x . f(5) = 15 - 6 = 9, f(2) = 6 - 15 = -9. f(5) - f(2) = 9 - (-9) = 18.
Related: Mathematics — Functions · All PYQ Banks