PrepWiser › Learn › Mathematics › Functions (Advanced)Functions (Advanced) — JEE Main PYQs & Practice Questions Functions (Advanced) is a Mathematics chapter in the JEE Main syllabus. This page brings together 72 previous-year and practice questions on Functions (Advanced), organised into 4 topics: Domain and Range, Composite Functions, Inverse Functions and Functional Equations. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Chapter weightage : how many questions each chapter had per shift in the 2024–26 papers.
Domain and Range If the function f:(-∞,-1] →(a, b] defined by f(x)=e^(x³-3 x+1) is one - one and onto… If the range of the function f(x) = (5-x)/(x² - 3x + 2) , x ≠ 1, 2, is (-∞ , α] ∪ [β, ∞)… If the domain of the function f(x)=log ₑ(4 x²+11 x+6)+sin ⁻¹(4 x+3)+cos ⁻¹((10 x+6)/3)… If the functions are defined as f(x) = √x and g(x) = √(1 - x), then what is the common… If the domain of the function f(x)=√(x²-25)/(4-x²)+log ₁₀(x²+2 x-15) is (-∞, α) ∪[β, ∞)… If the domain of the function f(x)=√log_((0.6))(|(2x-5)/(x²-4)|) is (-∞,a]∪ {b}∪ [c,d)∪… If the domain of the function f(x)=log ₑ((2 x+3)/(4 x²+x-3))+cos ⁻¹((2 x-1)/(x+2)) is… If the domain of the function log₅(18x - x² - 77) is (α, β) and the domain of the… Let f:[0,3] → A be defined by f(x)=2 x³-15 x²+36 x+7 and g:[0, ∞) → B be defined by… The domain of f(x) = (log ₍ₓ₊₁₎(x - 2))/(e^(2log ₑx) - (2x + 3)),x ∈ ℝ is Let the domain of the function f(x)=log₃ log₅(7-log₂(x²-10x+85))+sin⁻¹(|(3x-7)/(17-x)|)… Let f(x)=1/(7-sin 5 x) be a function defined on R. Then the range of the function f(x)… If the domain of the function f(x)=1/√(10+3 x-x²)+1/√(x+|x|) is (a, b), then (1+a)²+b²… Let the domains of the functions f(x)=log ₄ log ₃ log ₇(8-log ₂(x²+4 x+5)) and g(x)=sin… Let f:ℝ→ℝ be a function defined by f(x) = log _(√m){ √2 (sin x - cos x) + m - 2}, for… If the domain of the function f(x)=sin⁻¹((5-x)/(3+2x))+1/logₑ(10-x) is (-∞,α]∪… If the domain of the function f(x)=log ₇(1-log ₄(x²-9 x+18)) is (α, β) ∪(γ, o), then… The range of the function f(x)=√(3-x)+√(2+x) is : Let f: ℝ-{2,6} → ℝ be real valued function defined as f(x)=(x²+2 x+1)/(x²-8 x+12). Then… Composite Functions Inverse Functions The inverse of y = 5ˡᵒᵍˣ is : Let f : R - 3 → R - 1 be defined by f(x) = (x - 2)/(x - 3). Let g : R → R be given as… The inverse function of f(x) = (8²ˣ - 8⁻²ˣ)/(8²ˣ + 8⁻²ˣ), x ∈ (-1, 1), is : Let f(x)=x⁵+2 e^(x / 4) for all x ∈ R. Consider a function g(x) such that (g ° f)(x)=x… Let f(x)=x⁵+2 x³+3 x+1, x ∈ R, and g(x) be a function such that g(f(x))=x for all x ∈ R… For the function f:[1,∞)→ [1,∞) defined by f(x)=(x-1)⁴+1, among the two statements: (I)… The inverse of f(x) = (3x - 2) / 4 is: Let f : R → R be defined as f(x) = x³ + x - 5. If g(x) is a function such that f(g(x)) =… Let α, β and γ be three positive real numbers. Let f(x)=α x⁵+β x³+γ x, x ∈ R and g: R →… Functional Equations Let f be a polynomial function such that log₂(f(x))=(log₂(2+2/3+2/9+… … ∞ ))·… Let f : R → R satisfy f(x + y) = 2ˣf(y) + 4ʸf(x), ∀x, y ∈ R. If f(2) = 3, then 14… Suppose f: ℝ →(0, ∞) be a differentiable function such that 5 f(x+y)=f(x) · f(y), ∀ x, y… Let f and g be functions satisfying f(x+y)=f(x)f(y),f(1)=7 and g(x+y)=g(xy),g(1)=1, for… Let f : R → R be a function defined by f(x) = 2e²ˣ/(e²ˣ + e). Then f( 1/100 ) + f( 2/100… If a function f satisfies f( m+n)=f( m)+f(n) for all m, n ∈ N and f(1)=1, then the… Let f(x) be a real differentiable function such that f(0)=1 and f(x+y)=f(x) f′(y)+f′(x)… Let f: ℝ-{0} → ℝ be a function satisfying f(x/y)=f(x)/f(y) for all x, y, f(y) ≠ 0. If… Let f: ℝ → ℝ be a function defined by f(x)=(2+3 a) x²+((a+2)/(a-1)) x+b, a ≠ 1. If… Let f be a function such that 3f(x)+2f(m/19x)=5x,x≠ 0, where m=Σᵢ₌₁⁹(i)². Then f(5)-f(2)… Suppose a differentiable function f(x) satisfies the identity f(x+y) = f(x) + f(y) + xy²… For a suitably chosen real constant a, let a function, f:R - { - a } → R be defined by… If a + α = 1, b + β = 2 and af(x) + α f( 1/x ) = bx + β/x,x ≠ 0, then the value of the… Let 5 f(x)+4 f(1/x)=1/x+3, x > 0. Then 18 ∫1² f(x) d x is equal to : Let f: ℝ-{0} → ℝ be a function such that f(x)-6 f(1/x)=35/(3 x)-5/2. If the lim _(x →… Let f : N → N be a function such that f(m + n) = f(m) + f(n) for every m, n∈N. If f(6) =… A function f(x) is given by f(x) = 5ˣ/(5ˣ + 5), then the sum of the series f( 1/20 ) +… Let f : R → R be defined as f(x + y) + f(x - y) = 2f(x)f(y),f( 1/2 ) = - 1. Then, the… Let f(x) be a function such that f(x+y)=f(x).f(y) for all x,y∈ ℕ. If f(1)=3 and Σₖ₌₁ⁿ… If f(x) = 2²ˣ/(2²ˣ + 2),x ∈ ℝ, then f( 1/2023 ) + f( 2/2023 ) + ... + f( 2022/2023 ) is… More Mathematics chapters Frequently asked questions How many Functions (Advanced) questions are there for JEE Main? PrepWiser has 72 Functions (Advanced) questions for JEE Main, grouped into 4 topics such as Domain and Range, Composite Functions and Inverse Functions.
Are these Functions (Advanced) questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Functions (Advanced) questions? Open any Functions (Advanced) question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.