JEE Main 2025 — Functions Questions with Solutions

Let the domains of the functions f(x)= ₄ ₃ ₇ (8- ₂ (x²+4 x+5 ) ) and g(x)= ⁻¹ ((7 x+10)/(x-2) ) be (α, β) and [γ, δ], r…

Number of functions f:\1,2, …, 100 →\0,1\, that assign 1 to exactly one of the positive integers less than or equal to…

Let f: R → R be a continuous function satisfying f(0)=1 and f(2 x)-f(x)=x for all x R. If n → ∞ \f(x)-f ((x)/(2ⁿ) ) \=G…

Let A=\1,2,3,4\ and B=\1,4,9,16\. Then the number of many-one functions f: A → B such that 1 f(~A) is equal to :

Let the domain of the function f(x)= ⁻¹ ((4 x+5)/(3 x-7) ) be [α, β] and the domain of g(x)= ₂ (2-6 ₂₇(2 x+5) ) be (γ,…

Let f:[0,3] → A be defined by f(x)=2 x³-15 x²+36 x+7 and g:[0, ∞) → B be defined by g(x)=x²⁰²⁵x²⁰²⁵+1. If both the func…

If the domain of the function f(x)= ₇ (1- ₄ (x²-9 x+18 ) ) is (α, β) (γ, δ), then α+β+γ+δ is equal to

Let f: R → R be a function defined by f(x)=(2+3 a) x²+ ((a+2)/(a-1) ) x+b, a ≠ 1 . If f(x+y)=f(x)+f(y)+1-(2)/(7) x y, t…

If the domain of the function ₅ (18 x-x²-77 ) is (α, β) and the domain of the function ₍x₋₁₎ ((2 x²+3 x-2)/(x²-3 x-4) )…

Let f: R-\0 →(-∞, 1) be a polynomial of degree 2, satisfying f(x) f ((1)/(x) )=f(x)+f ((1)/(x) ). If f(K)=-2 K, then th…