Functional Equations

JEE Main Mathematics · Continuity and Differentiability · 3 questions, latest first

• Let f: R-{0} → R be a function satisfying f(x/y)=(f(x))/(f(y)) for all x, y, f(y) ≠ 0. If f^′(1)=2024, then202430 January, Shift 2 · Q7
• Let for a differentiable function f:(0, ∞) → R, f(x)-f(y) ≥ log_e(x/y)+x-y, ∀ x, y ∈(0, ∞). Then Σ_n=1^20 f^′(1/n^2) is equal to…202427 January, Shift 1 · Q23
• 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)|…202329 January, Shift 1 · Q87