Domain and Range of Inverse Trigonometric Functions

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JEE Main 2003

The trigonometric equation $sin^{- 1} x = 2 sin^{- 1} a$ has a solution for

JEE Main 2002

The domain of $sin^{- 1} [lo g_{3} (x /3)]$ is

[1, 9]

(B)

[- 1, 9]

(C)

[- 9, 1]

(D)

[- 9, - 1]

JEE Advanced 2003

LEVELJEE Main

Domain of definition of the function $f (x) = sin^{- 1} (2 x) + π /6$ for real valued $x$ , is

(A)

[- 1/4, 1/2]

(B)

[- 1/2, 1/2]

(C)

[- 1/2, 1/9]

(D)

[- 1/4, 1/4]

JEE Advanced 1984

LEVELJEE Main

The domain of the function $f (x) = sin^{- 1} (lo g_{2} \frac{x ^{2}}{2})$ is given by .........

JEE Main 2020 - 2 Sep (Morning)

LEVELJEE Main

The domain of the function $f (x) = sin^{- 1} (\frac{∣ x ∣ + 5}{x ^{2} + 1})$ is $(- \infty, - a] \cup [a, \infty)$ . Then $a$ is equal to :

(A)

\frac{1 + 17}{2}

(B)

\frac{17 + 1}{2}

(C)

\frac{17 - 1}{2}

(D)

\frac{17}{2}

JEE Main 2021 (22 July Shift 1)

LEVELJEE Main

If the domain of the function $f (x) = \frac{c o s ^{- 1} x ^{2} - x + 1}{s i n ^{- 1} ( \frac{2 x - 1}{2} )}$ is the interval $(α, β]$ , then $α + β$ is equal to :

(A)

\frac{3}{2}

(B)

(C)

\frac{1}{2}

(D)

JEE Main 2021 (31 Aug Shift 2)

LEVELJEE Advanced

The domain of the function $f (x) = sin^{- 1} (\frac{3 x ^{2} + x - 1}{( x - 1 ) ^{2}}) + cos^{- 1} (\frac{x - 1}{x + 1})$ is :

(A)

[0, \frac{1}{4}]

(B)

[- 2, 0] \cup [\frac{1}{4}, \frac{1}{2}]

(C)

[\frac{1}{4}, \frac{1}{2}] \cup {0}

(D)

[0, \frac{1}{2}]

JEE Main 2021 (26 Aug Shift 2)

LEVELJEE Main

The domain of the function $cosec^{- 1} (\frac{1 + x}{x})$ is :

(A)

(- 1, - \frac{1}{2}] \cup (0, \infty)

(B)

[- \frac{1}{2}, 0) \cup [1, \infty)

(C)

(- \frac{1}{2}, \infty) - {0}

(D)

[- \frac{1}{2}, \infty) - {0}

JEE Main 2021 (18 March Shift 1)

LEVELJEE Main

The real valued function $f (x) = \frac{cosec ^{- 1} x}{x - [ x ]}$ , where $[x]$ denotes the greatest integer less than or equal to $x$ , is defined for all $x$ belonging to:

(A)

all reals except integers

(B)

all non-integers except the interval

[- 1, 1]

(C)

all integers except 0,-1,1

(D)

all reals except the Interval

[- 1, 1]

JEE Main 2022 (29 June Shift 1)

LEVELJEE Main

The domain of the function $cos^{- 1} (\frac{2 s i n ^{- 1} ( \frac{1}{4 x ^{2} - 1} )}{π})$ is:

(A)

R - {- \frac{1}{2}, \frac{1}{2}}

(B)

(- \infty, - 1] \cup [1, \infty) \cup {0}

(C)

(- \infty, - \frac{1}{2}) \cup (\frac{1}{2}, \infty) \cup {0}

(D)

(- \infty, - \frac{1}{2}] \cup [\frac{1}{2}, \infty] \cup {0}

JEE Main 2022 (28 July Shift 1)

LEVELJEE Main

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f (x) = cos^{- 1} (\frac{x ^{2} - 4 x + 2}{x ^{2} + 3})$ is :

(A)

(- \infty, \frac{1}{4}]

(B)

[- \frac{1}{4}, \infty)

(C)

(- \frac{1}{3}, \infty)

(D)

(- \infty, \frac{1}{3}]

JEE Main 2022 (29 July Shift 2)

LEVELJEE Main

The domain of the function $f (x) = sin^{- 1} (\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 7})$ is :

(A)

[1, \infty)

(B)

(- 1, 2]

(C)

[- 1, \infty)

(D)

(- \infty, 2]

JEE Main 2023 (10 April Shift 2)

LEVELJEE Main

If the domain of the function $f (x) = sec^{- 1} (\frac{2 x}{5 x + 3})$ is $[α, β) \cup (γ, δ]$ , then $∣3 α + 10 (β + γ) + 21 δ ∣$ is equal to

JEE Main 2023 (12 April Shift 1)

LEVELJEE Advanced

Let $D$ be the domain of the function $f (x) = sin^{- 1} (lo g_{3 x} (\frac{6 + 2 l o g _{3} x}{- 5 x}))$ . If the range of the function $g : D \to R$ defined by $g (x) = x - [x]$ , ( $[x]$ is the greatest integer function), is $(α, β)$ , then $α^{2} + \frac{5}{β}$ is equal to

JEE Main 2023 (13 April Shift 2)

LEVELBoard

The range of $f (x) = 4 sin^{- 1} (\frac{x ^{2}}{x ^{2} + 1})$ is

(A)

[0, 2 π]

(B)

[0, π]

(C)

[0, 2 π)

(D)

[0, π)

JEE Main 2023 (15 April Shift 1)

LEVELJEE Main

If the domain of the function $f (x) = lo g_{e} (4 x^{2} + 11 x + 6) + sin^{- 1} (4 x + 3) + cos^{- 1} (\frac{10 x + 6}{3})$ is $(α, β]$ , then $36∣ α + β ∣$ is equal to

JEE Main 2024 (09 Apr Shift 1)

LEVELJEE Main

If the domain of the function $f (x) = sin^{- 1} (\frac{x - 1}{2 x + 3})$ is $R - (α, β)$ , then $12 α β$ is equal to :

JEE Main 2024 (30 Jan Shift 1)

LEVELJEE Main

If the domain of the function $f (x) = cos^{- 1} (\frac{2 - ∣ x ∣}{4}) + (lo g_{e} (3 - x))^{- 1}$ is $[- α, β) - {γ}$ , then $α + β + γ$ is equal to :

JEE Main 2025 (January)

LEVELJEE Main

Let $[\cdot]$ denote the greatest integer less than or equal to $\cdot$ . Then the domain of $f (x) = sec^{- 1} (2 [x] + 1)$ is:

(A)

(- \infty, - 1] \cup [0, \infty)

(B)

(- \infty, - 1] \cup [1, \infty)

(C)

(- \infty, \infty)

(D)

(- \infty, \infty) - {0}

JEE Main 2026 (24 January Shift 2)

LEVELJEE Main

If the domain of the function $f (x) = sin^{- 1} (\frac{1}{x ^{2} - 2 x - 2})$ , is $(- \infty, α] \cup [β, γ] \cup [δ, \infty)$ , then $α + β + γ + δ$ is equal to

JEE Main 2026 (21 January Shift 1)

LEVELJEE Main

If the domain of the function $f (x) = cos^{- 1} (\frac{2 x - 5}{11 - 3 x}) + sin^{- 1} (2 x^{2} - 3 x + 1)$ is the interval $[α, β]$ , then $α + 2 β$ is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The trigonometric equation sin−1x=2sin−1a has a solution for

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The domain of sin−1[log3​(x/3)] is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Domain of definition of the function f(x)=sin−1(2x)+π/6​ for real valued x, is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The domain of the function f(x)=sin−1(log2​2x2​) is given by .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The domain of the function f(x)=sin−1(x2+1∣x∣+5​) is (−∞,−a]∪[a,∞). Then a is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the domain of the function f(x)=sin−1(22x−1​)​cos−1x2−x+1​​ is the interval (α,β], then α+β is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The domain of the function f(x)=sin−1((x−1)23x2+x−1​)+cos−1(x+1x−1​) is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The domain of the function cosec−1(x1+x​) is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The real valued function f(x)=x−[x]​cosec−1x​, where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The domain of the function cos−1(π2sin−1(4x2−11​)​) is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Considering only the principal values of the inverse trigonometric functions, the domain of the function f(x)=cos−1(x2+3x2−4x+2​) is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The domain of the function f(x)=sin−1(x2+2x+7x2−3x+2​) is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the domain of the function f(x)=sec−1(5x+32x​) is [α,β)∪(γ,δ], then ∣3α+10(β+γ)+21δ∣ is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The range of f(x)=4sin−1(x2+1x2​) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the domain of the function f(x)=loge​(4x2+11x+6)+sin−1(4x+3)+cos−1(310x+6​) is (α,β], then 36∣α+β∣ is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the domain of the function f(x)=sin−1(2x+3x−1​) is R−(α,β), then 12αβ is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the domain of the function f(x)=cos−1(42−∣x∣​)+(loge​(3−x))−1 is [−α,β)−{γ}, then α+β+γ is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let [⋅] denote the greatest integer less than or equal to ⋅ . Then the domain of f(x)=sec−1(2[x]+1) is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the domain of the function f(x)=sin−1(x2−2x−21​), is (−∞,α]∪[β,γ]∪[δ,∞), then α+β+γ+δ is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the domain of the function f(x)=cos−1(11−3x2x−5​)+sin−1(2x2−3x+1) is the interval [α,β], then α+2β is equal to :

The trigonometric equation $sin^{- 1} x = 2 sin^{- 1} a$ has a solution for

The domain of $sin^{- 1} [lo g_{3} (x /3)]$ is

Domain of definition of the function $f (x) = sin^{- 1} (2 x) + π /6$ for real valued $x$ , is

The domain of the function $f (x) = sin^{- 1} (lo g_{2} \frac{x ^{2}}{2})$ is given by .........

The domain of the function $f (x) = sin^{- 1} (\frac{∣ x ∣ + 5}{x ^{2} + 1})$ is $(- \infty, - a] \cup [a, \infty)$ . Then $a$ is equal to :

If the domain of the function $f (x) = \frac{c o s ^{- 1} x ^{2} - x + 1}{s i n ^{- 1} ( \frac{2 x - 1}{2} )}$ is the interval $(α, β]$ , then $α + β$ is equal to :

The domain of the function $f (x) = sin^{- 1} (\frac{3 x ^{2} + x - 1}{( x - 1 ) ^{2}}) + cos^{- 1} (\frac{x - 1}{x + 1})$ is :

The domain of the function $cosec^{- 1} (\frac{1 + x}{x})$ is :

The real valued function $f (x) = \frac{cosec ^{- 1} x}{x - [ x ]}$ , where $[x]$ denotes the greatest integer less than or equal to $x$ , is defined for all $x$ belonging to:

The domain of the function $cos^{- 1} (\frac{2 s i n ^{- 1} ( \frac{1}{4 x ^{2} - 1} )}{π})$ is:

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f (x) = cos^{- 1} (\frac{x ^{2} - 4 x + 2}{x ^{2} + 3})$ is :

The domain of the function $f (x) = sin^{- 1} (\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 7})$ is :

If the domain of the function $f (x) = sec^{- 1} (\frac{2 x}{5 x + 3})$ is $[α, β) \cup (γ, δ]$ , then $∣3 α + 10 (β + γ) + 21 δ ∣$ is equal to

The range of $f (x) = 4 sin^{- 1} (\frac{x ^{2}}{x ^{2} + 1})$ is

If the domain of the function $f (x) = lo g_{e} (4 x^{2} + 11 x + 6) + sin^{- 1} (4 x + 3) + cos^{- 1} (\frac{10 x + 6}{3})$ is $(α, β]$ , then $36∣ α + β ∣$ is equal to

If the domain of the function $f (x) = sin^{- 1} (\frac{x - 1}{2 x + 3})$ is $R - (α, β)$ , then $12 α β$ is equal to :

If the domain of the function $f (x) = cos^{- 1} (\frac{2 - ∣ x ∣}{4}) + (lo g_{e} (3 - x))^{- 1}$ is $[- α, β) - {γ}$ , then $α + β + γ$ is equal to :

Let $[\cdot]$ denote the greatest integer less than or equal to $\cdot$ . Then the domain of $f (x) = sec^{- 1} (2 [x] + 1)$ is:

If the domain of the function $f (x) = sin^{- 1} (\frac{1}{x ^{2} - 2 x - 2})$ , is $(- \infty, α] \cup [β, γ] \cup [δ, \infty)$ , then $α + β + γ + δ$ is equal to

If the domain of the function $f (x) = cos^{- 1} (\frac{2 x - 5}{11 - 3 x}) + sin^{- 1} (2 x^{2} - 3 x + 1)$ is the interval $[α, β]$ , then $α + 2 β$ is equal to :