Question

Find the domain of the function f(x) = ( 5 pi sin ^-1 x - 6(sin^-1 x)²)½​

Answer 1

Answer:

Here, f(x)=sin−1(2x)+6π, to find domain,

we must have,

sin−1(2x)+2π>0(but−2π≤sin−1θ≤2π)

Therefore, −6π≤sin−1(2x)≤sin2π

⇒sin(−6π)≤2x≤sin(2π)

⇒−21≤2x≤1

⇒−41≤x≤21

⇒xϵ[−41,21].