Domain and Range of a Function

JEE Main Mathematics · Relations and Functions · 24 questions, latest first

• The sum of all the elements in the range of f(x)=Sgn( sin x)+Sgn( cos x)+Sgn( tan x)+Sgn( cot x), x ≠ (n π)/2, n ∈ Z, where…202628 January, Shift 2 · Q1
• If the domain of the function f(x)= log_(10 x^2-17 x+7)(18 x^2-11 x+1) is (-∞, a) ∪(b, c) ∪(d, ∞)-{e}, then 90(a+b+c+d+e) equals:202624 January, Shift 1 · Q2
• Let the domain of the function f(x)= log_3 log_5(7- log_2(x^2-10 x+85))+ sin^-1(|(3 x-7)/(17-x)|) be (α, β]. Then α+β is equal to:202622 January, Shift 2 · Q4
• If the domain of the function f(x)= sin^-1((5-x)/(3+2 x))+1/(log_e(10-x)) is (-∞, α] ∪[β, γ)-{δ}, then 6(α+β+γ+δ) is equal to202622 January, Shift 1 · Q2
• If the domain of the function f(x)= cos^-1((2 x-5)/(11-3 x))+ sin^-1(2 x^2-3 x+1) is the interval [α, β], then α+2 β is equal to:202621 January, Shift 1 · Q2
• Let the domain of the function f(x)= cos^-1((4 x+5)/(3 x-7)) be [α, β] and the domain of g(x)= log_2(2-6 log_27(2 x+5)) be (γ,…20258 April, Shift 2 · Q21
• If the range of the function f(x)=(5-x)/(x^2-3 x+2), x ≠ 1,2, is (-∞, α] ∪[β, ∞), then α^2+β^2 is equal to:20257 April, Shift 2 · Q2
• Let the domains of the functions f(x)= log_4 log_3 log_7(8- log_2(x^2+4 x+5)) and g(x)= sin^-1((7 x+10)/(x-2)) be (α, β) and [γ,…20254 April, Shift 2 · Q1
• If the domain of the function f(x)= log_7(1- log_4(x^2-9 x+18)) is (α, β) ∪(γ, δ), then α+β+γ+δ is equal to20253 April, Shift 2 · Q2
• If the domain of the function f(x)= log_e((2 x-3)/(5+4 x))+ sin^-1((4+3 x)/(2-x)) is [α, β), then α^2+4 β is equal to20253 April, Shift 1 · Q2
• If the domain of the function f(x)=1/(√(10+3 x-x^2))+1/(√(x+|x|)) is (a, b), then (1+a)^2+b^2 is equal to:20252 April, Shift 2 · Q1
• If the domain of the function log_5(18 x-x^2-77) is (α, β) and the domain of the function log_(x-1)((2 x^2+3 x-2)/(x^2-3 x-4)) is…202529 January, Shift 2 · Q1
• Let f:[0,3] → A be defined by f(x)=2 x^3-15 x^2+36 x+7 and g:[0, ∞) → B be defined by g(x)=(x^2025)/(x^2025+1). If both the…202528 January, Shift 2 · Q2
• If the domain of the function sin^-1((3 x-22)/(2 x-19))+ log_e((3 x^2-8 x+5)/(x^2-3 x-10)) is (α, β], then 3 α+10 β is equal to:20244 April, Shift 1 · Q1
• If the domain of the function f(x)=(√(x^2-25))/((4-x^2))+ log_10(x^2+2 x-15) is (-∞, α) ∪[β, ∞), then α^2+β^3 is equal to:20241 February, Shift 2 · Q1
• If the function f:(-∞,-1] →(a, b] defined by f(x)=e^x^3-3 x+1 is one - one and onto, then the distance of the point P(2 b+4, a+2)…202431 January, Shift 2 · Q1
• If the domain of the function f(x)= log_e((2 x+3)/(4 x^2+x-3))+ cos^-1((2 x-1)/(x+2)) is (α, β], then the value of 5 β-4 α is…202430 January, Shift 2 · Q1
• If the domain of the function f(x)= cos^-1((2-|x|)/4)+{ log_e(3-x)}^-1 is [-α, β)-{γ}, then α+β+γ is equal to:202430 January, Shift 1 · Q1
• If the domain of the function f(x)= log_e(4 x^2+11 x+6)+ sin^-1(4 x+3)+ cos^-1((10 x+6)/3) is (α, β], then 36|α+β| is equal to202315 April, Shift 1 · Q1
• Let D be the domain of the function f(x)= sin^-1( log_3 x((6+2 log_3 x)/(-5 x))). If the range of the function g: D → R defined…202312 April, Shift 1 · Q1
• If domain of the function log_e((6 x^2+5 x+1)/(2 x-1))+ cos^-1((2 x^2-3 x+4)/(3 x-5)) is (α, β) ∪(γ, δ], then 18(α^2+β^2+γ^2+δ^2)…20238 April, Shift 2 · Q21
• Let f: R-{2,6} → R be real valued function defined as f(x)=(x^2+2 x+1)/(x^2-8 x+12). Then range of f is202331 January, Shift 2 · Q72
• The range of the function f(x)=√(3-x)+√(2+x) is:202330 January, Shift 2 · Q61
• The domain of f(x)=(log_(x+1)(x-2))/(e^2 log_e x-(2 x+3)), x ∈ R is202329 January, Shift 1 · Q61