Let f be a function such that 3 f ( x )+2 f (frac m 19 x )=5 x , x neq 0 , where m=sum i=1 9 (i) 2 . Then f(5)-f(2) is equal to :

Mathematics · Functions

JEE Main 2026 — 24 January, Evening Shift — Question 17

Let f be a function such that $3 \mathrm{f}(\mathrm{x})+2 \mathrm{f}\left(\frac{\mathrm{m}}{19 \mathrm{x}}\right)=5 \mathrm{x}$ , $x \neq 0$ , where $m=\sum_{i=1}^{9}(i)^{2}$ . Then $f(5)-f(2)$ is equal to :

Option A:
$-9$
Option B:
$36$
Option C:
$18$
Correct
Option D:
$9$

Answer: C

Step-by-step solution

$\mathrm{m}=\frac{9 \times 10 \times 19}{6}=15 \times 19$

$3 f(x)+2 f\left(\frac{15}{x}\right)=5 x$

Replace x by $\frac{15}{\mathrm{x}}$

$3 f\left(\frac{15}{x}\right)+2 f(x)=\frac{75}{x}$

$9 f(x)-4 f(x)=15 x-\frac{150}{x}$

$5 f(x)=15 x-\frac{150}{x}$

$\mathrm{f}(\mathrm{x})=3 \mathrm{x}-\frac{30}{\mathrm{x}}$

$f(5)=15-\frac{30}{5}=9$

$f(2)=6-15=-9$

$f(5)-f(2)=18$

Answer key and solution verified before publishing.

Practise Functions

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2026
Paper: 24 January, Evening Shift
Subject: Mathematics
Chapter: Functions
Topic: Functional Equations

If the domain of the function f(x)=sin ^-1 (frac1x^2-2 x-2 ) , is (-infty, alpha] cup[beta, gamma] cup[delta, infty) , then…

Answer: C

Step-by-step solution

Practise Functions

More Functions questions from this paper