Advertisements
Advertisements
प्रश्न
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Advertisements
उत्तर
For `cos^-1 (x^2 - 4)` to be defined
`-1 ≤ x^2 - 4 ≤ 1`
⇒ `3 ≤ x^2 ≤ 5`
⇒ `x in [- sqrt5, - sqrt3 ] cup [sqrt3, sqrt5 ] `
Hence, the domain of `f(x) is [-sqrt5, -sqrt3] cup [sqrt3, sqrt5]`.
APPEARS IN
संबंधित प्रश्न
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin4)`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)+1)/x},x !=0`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
`tan^-1x+2cot^-1x=(2x)/3`
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Prove that:
`tan^-1 (2ab)/(a^2-b^2)+tan^-1 (2xy)/(x^2-y^2)=tan^-1 (2alphabeta)/(alpha^2-beta^2),` where `alpha=ax-by and beta=ay+bx.`
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
If \[3\sin^{- 1} \left( \frac{2x}{1 + x^2} \right) - 4 \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + 2 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) = \frac{\pi}{3}\] is equal to
If tan−1 (cot θ) = 2 θ, then θ =
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
The value of sin `["cos"^-1 (7/25)]` is ____________.
