Find the domain of each of the following functions:f(x) = sin–1x + s

1.	Find the domain of each of the following functions:f(x) = sin–1x + sin–12x
Answer» Domain of sin^-1lies in the interval [–1, 1]. -1 ≤ x ≤ 1 Therefore, the domain of sin^-12x lies in the interval \([-\frac{\pi}2,\frac{\pi}2]\) -1 ≤ 2x ≤ 1 \(-\frac 12\leq x\le\frac 12\) The domain of sin^–1x + sin^–12x is the intersection of the domains of sin^–1x and sin^–12x. So, Domain of sin^-1x + sin^-12x is \([-\frac 12,\frac 12].\)

Find the domain of each of the following functions:f(x) = sin–1x + sin–12x

Answer»

Domain of sin^-1lies in the interval [–1, 1].

-1 ≤ x ≤ 1

Therefore, the domain of sin^-12x lies in the interval \([-\frac{\pi}2,\frac{\pi}2]\)

-1 ≤ 2x ≤ 1

\(-\frac 12\leq x\le\frac 12\)

The domain of sin^–1x + sin^–12x is the intersection of the domains of sin^–1x and sin^–12x.

So, Domain of sin^-1x + sin^-12x is \([-\frac 12,\frac 12].\)