Advertisements
Advertisements
Question
The domain of the function y = sin–1 (– x2) is ______.
Options
[0, 1]
(0, 1)
[–1, 1]
φ
Solution
The domain of the function y = sin–1 (– x2) is [–1, 1].
Explanation:
y = sin–1(– x2)
⇒ siny = – x2
i.e. – 1 ≤ – x2 ≤ 1 ......(Since – 1 ≤ sin y ≤ 1)
⇒ 1 ≥ x2 ≥ – 1
⇒ 0 ≤ x2 ≤ 1
⇒ |x| ≤ 1
i.e. – 1 ≤ x ≤ 1
APPEARS IN
RELATED QUESTIONS
Find the domain of the following function:
`f(x) = sin^-1x + sinx`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`
In ΔABC prove that `(b + c - a) tan "A"/(2) = (c + a - b)tan "B"/(2) = (a + b - c)tan "C"/(2)`.
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
Find the principal value of the following: sin-1 `(1/sqrt(2))`
Find the principal value of the following: cos- 1`(-1/2)`
Evaluate the following:
`cos^-1(1/2) + 2sin^-1(1/2)`
Prove the following:
`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).
`tan^-1(tan (7pi)/6)` = ______
Evaluate cot(tan−1(2x) + cot−1(2x))
Evaluate:
`sin[cos^-1 (3/5)]`
Find the principal value of the following:
cosec-1 (2)
Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.
The value of cot `(tan^-1 2x + cot^-1 2x)` is ______
If sin `(sin^-1 1/3 + cos^-1 x) = 1`, then the value of x is ______.
`cos(2sin^-1 3/4+cos^-1 3/4)=` ______.
The value of `sin^-1(cos (53pi)/5)` is ______
When `"x" = "x"/2`, then tan x is ____________.
`("cos" 8° - "sin" 8°)/("cos" 8° + "sin" 8°)` is equal to ____________.
`"sin" ["cot"^-1 {"cos" ("tan"^-1 "x")}] =` ____________.
If a = `(2sin theta)/(1 + costheta + sintheta)`, then `(1 + sintheta - costheta)/(1 + sintheta)` is
If A = `[(cosx, sinx),(-sinx, cosx)]`, then A1 A–1 is
What is the value of `sin^-1(sin (3pi)/4)`?
If f(x) = x5 + 2x – 3, then (f–1)1 (–3) = ______.
If f'(x) = x–1, then find f(x)
`sin[π/3 + sin^-1 (1/2)]` is equal to ______.
Solve for x:
5tan–1x + 3cot–1x = 2π
