Domain of definition of the function f x -sin -12 x -6 for real valued x- isA- -1-4- 1-2-B- -1-2- 1-9C-D- -1- 1-

The correct option is A [ 1/4, 1/2 ]Here, f(x)=√(sin^ 1(2x)+π/6), to find domain we must have, sin^ 1(2x)+ π/6≥ 0 [ but π/2≤ sin^ 1θ≤π/2 ] π/6≤ sin^ 1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Domain

Domain of def...

Question

Domain of definition of the function $f (x) = \sqrt{s i n^{- 1} (2 x) + \frac{π}{6}}$ for real valued x, is

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(- \frac{1}{2}, \frac{1}{9})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $[- \frac{1}{4}, \frac{1}{2}]$
Here, $f (x) = \sqrt{s i n^{- 1} (2 x) + \frac{π}{6}}$ , to find domain we must have,
$s i n^{- 1} (2 x) + \frac{π}{6} \geq 0 [b u t - \frac{π}{2} \leq s i n^{- 1} θ \leq \frac{π}{2}] - \frac{π}{6} \leq s i n^{- 1} (2 x) \leq \frac{π}{2} s i n (- \frac{π}{6}) \leq 2 n \leq s i n \frac{π}{2} \frac{- 1}{2} \leq 2 x \leq 1 \frac{- 1}{4} \leq x \leq \frac{1}{2} ∵ x ϵ [- \frac{1}{4}, \frac{1}{2}]$

Suggest Corrections

Similar questions

Q. Domain of definition of the function

f (x) = \sqrt{s i n^{- 1} (2 x) + \frac{π}{6}}

for real valued x, is

Q. Domain of definition of the function

f (x) = \sqrt{s i n^{- 1} (2 x) + \frac{π}{6}}

for real valued x, is

Q. Domain of definition of the function

f (x) = \sqrt{{sin}^{- 1} (2 x) + \frac{π}{6}}

for real valued

x

, is

Q. The domain of the function

f (x) = \sqrt{{sin}^{- 1} (2 x) + \frac{π}{6}}

for real

x

, is

Q. Let

f (x)

be a real valued function, then the domain of

f (x) = \sqrt{x - \sqrt{1 - x^{2}}}

Join BYJU'S Learning Program

Domain of definition of the function f(x)=√sin−1(2x)+π6 for real valued x, is

The correct option is A [−14, 12]Here, f(x)=√sin−1(2x)+π6, to find domain we must have, sin−1(2x)+π6≥0 [but−π2≤sin−1θ≤π2]−π6≤sin−1(2x)≤π2sin(−π6)≤2n≤sinπ2−12≤2x≤1−14≤x≤12∵ xϵ[−14,12]

Domain of definition of the function $f (x) = \sqrt{s i n^{- 1} (2 x) + \frac{π}{6}}$ for real valued x, is