Advertisements
Advertisements
प्रश्न
Find the domain of the following function:
`f(x)=sin^-1x^2`
Advertisements
उत्तर
To the domain of sin-1 which is [−1, 1]
∴ x2 ∈ [0, 1] as x2 can not be negative
∴ x ∈ [-1, 1]
Hence, the domain is [−1, 1]
APPEARS IN
संबंधित प्रश्न
Show that `2sin^-1(3/5) = tan^-1(24/7)`
Find the principal value of the following:
tan−1 (−1)
`sin^-1 1/2-2sin^-1 1/sqrt2`
Evaluate the following:
`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`
Evaluate the following:
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`
Evaluate: tan `[ 2 tan^-1 (1)/(2) – cot^-1 3]`
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).
Find the principal solutions of the following equation:
tan 5θ = -1
sin−1x − cos−1x = `pi/6`, then x = ______
The principal value of sin−1`(1/2)` is ______
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
Evaluate cot(tan−1(2x) + cot−1(2x))
Prove that cot−1(7) + 2 cot−1(3) = `pi/4`
Solve `tan^-1 2x + tan^-1 3x = pi/4`
Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`
Prove that `tan^-1 (m/n) - tan^-1 ((m - n)/(m + n)) = pi/4`
A man standing directly opposite to one side of a road of width x meter views a circular shaped traffic green signal of diameter ‘a’ meter on the other side of the road. The bottom of the green signal Is ‘b’ meter height from the horizontal level of viewer’s eye. If ‘a’ denotes the angle subtended by the diameter of the green signal at the viewer’s eye, then prove that α = `tan^-1 (("a" + "b")/x) - tan^-1 ("b"/x)`
lf `sqrt3costheta + sintheta = sqrt2`, then the general value of θ is ______
The principle solutions of equation tan θ = -1 are ______
`sin^2(sin^-1 1/2) + tan^2 (sec^-1 2) + cot^2(cosec^-1 4)` = ______.
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then θ = ______
The value of `sin^-1(cos (53pi)/5)` is ______
The domain of the function y = sin–1 (– x2) is ______.
Solve the following equation `cos(tan^-1x) = sin(cot^-1 3/4)`
Prove that `tan^-1 1/4 + tan^-1 2/9 = sin^-1 1/sqrt(5)`
`("cos" 8° - "sin" 8°)/("cos" 8° + "sin" 8°)` is equal to ____________.
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
`sin[π/3 - sin^-1 (-1/2)]` is equal to:
If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.
If A = `[(cosx, sinx),(-sinx, cosx)]`, then A1 A–1 is
If |Z1| = |Z2| and arg (Z1) + arg (Z2) = 0, then
The inverse of `f(x) = sqrt(3x^2 - 4x + 5)` is
Assertion (A): The domain of the function sec–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`
Reason (R): sec–1(–2) = `- pi/4`
`cot^-1(sqrt(cos α)) - tan^-1 (sqrt(cos α))` = x, then sin x = ______.
If sin–1x – cos–1x = `π/6`, then x = ______.
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
