Domain, range and principal values

JEE Main Mathematics · Inverse Trigonometric Functions · 9 questions, latest first

• Let α=3 sin^-1(6/11) and β=3 cos^-1(4/9), where inverse trigonometric functions take only the principal values. Given below are…20268 April, Shift 2 · Q12
• Let [·] denote the greatest integer function. If the domain of the function f(x)= sin^-1((x+[x])/3) is [α, β), then α^2+β^2 is…20266 April, Shift 1 · Q1
• Let [·] denote the greatest integer function. If the domain of the function f(x)= cos^-1((4 x+2[x])/3) is [α, β], then 12(α+β) is…20264 April, Shift 1 · Q1
• If the domain of the function f(x)= sin^-1(1/(x^2-2 x-2)), is (-∞, α] ∪[β, γ] ∪[δ, ∞), then α+β+γ+δ is equal to202624 January, Shift 2 · Q1
• Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x)= sec^-1(2[x]+1) is:202528 January, Shift 2 · Q1
• If the domain of the function f(x)= sin^-1((x-1)/(2 x+3)) is R-(α, β), then 12 α β is equal to:20249 April, Shift 1 · Q1
• The range of f(x)=4 sin^-1(x^2/(x^2+1)) is202313 April, Shift 2 · Q1
• If the domain of the function f(x)= sec^-1((2 x)/(5 x+3)) is [α, β) U(γ, δ], then |3 α+10(β+γ)+21 δ| is equal to ____.202310 April, Shift 2 · Q21
• tan^-1((1+√3)/(3+√3))+ sec^-1(√((8+4 √3)/(6+3 √3))) is equal to:202324 January, Shift 1 · Q67