Question
Let f(x)= cases a x^ 2 +2 a x+3 4 x^ 2 +4 x-3 &, x - 3 2 , 1 2 \\ ~b &, x=- 3 2 , 1 2 cases be continuous at x=- 3 2 . If f f(x)= 7 5 , then x is equal to:
JEE Main
Mathematics
Continuity and Differentiability
2026
JEE Main 2026 (23 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 4
- B. 0
- C. 2
- D. 1
Answer
D. 1
Step-by-step solution
4x^2+4x-3 = (2x+3)(2x-1). For continuity at x = -3/2, numerator must vanish there: a(9/4) - 3a + 3 = 0 a = 4. f(x) = (2x+1)(2x+3) (2x+3)(2x-1) = 2x+1 2x-1 for x -3/2. f f(x) = f\! ( 2x+1 2x-1 ) = 6x+1 2x+3 . 6x+1 2x+3 = 7 5 30x+5 = 14x+21 x = 1.
Related: Mathematics — Continuity and Differentiability · All PYQ Banks