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

Question

Domain of definition of the function f(x) = √sin-1 (2x) + (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)]

Tardigrade Admin · Accepted Answer

-(π/6) le sin-1(2x) le (π/2) ⇒ -(1/2) le 2x le 1 ⇒ x ∈ [-(1/4), (1/2)]

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

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

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

$[- \frac{1}{2}, \frac{1}{9}]$

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

$- \frac{π}{6} \leq s i n^{- 1} (2 x) \leq \frac{π}{2} \Rightarrow - \frac{1}{2} \leq 2 x \leq 1 \Rightarrow x \in [- \frac{1}{4}, \frac{1}{2}]$

Q. Domain of definition of the function f(x)=sin−1(2x)+6π​​ for real valued x, is

[−41​,21​]

[−21​,21​]

[−21​,91​]

[−41​,41​]