Verified Solution • 2025–26 Session moderate QJEEM23Ma5220: JEE Main 2023 Mathematics - Class 12 JEEM23Ma5220 Solution: Let f : R → R be a differentiable function that satisfies the… Let f:R→R be a differentiable function that satisfies the relation f(x+y)=f(x)+f(y)−1,∀x,y∈R. If f′(0)=2, then |f(−2)| is equal to ___________. Step-by-Step Verified Solution f(x+y)=f(x)+f(y)−1f(x+y)=f(x)+f(y)-1f(x+y)=f(x)+f(y)−1 f′(x)=limh→0f(x+h)−f(x)hf′(x)=limh→0f(h)−f(0)h=f′(0)=2f′(x)=2⇒dy=2dxy=2x+Cx=0,y=1,c=1y=2x+1|f(−2)|=|−4+1|=|−3|=3 Related Learning Resources & Exam Preparation JEE Main PYQ Question Bank Browse year-wise authentic previous years' questions with solutions Authentic CBT Mock Tests Simulate official exam environment with live timer and percentile scoring