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JEE 2023 Mathematics PYQ — Let satisfy . If , find .… | Mathem Solvex

A.
3
(Correct Answer)
B.
2
C.
1
D.
0

Correct Answer:

3

Explanation

Solution:

Differentiate with respect to $y$ : $f'(x+y) = f'(y)$ .
Set $y=0$ : $f'(x) = f'(0) = 2$ .
Integrate: $f(x) = 2x + c$ .
Find $c$ : From the original relation, $f(0+0) = f(0) + f(0) - 1 \implies f(0) = 1$ .

$1 = 2(0) + c \implies c = 1$

So, $f(x) = 2x + 1$ .
Calculate $|f(-2)|$ :

$|f(-2)| = |2(-2) + 1| = |-3| = 3$

Final Answer:

|f(-2)| = 3

JEE 2023 — Mathematics PYQ

Choose the correct answer:

Explanation

Explanation