What is the domain of $y=3/2 arcsin(2x+.5)$ ?

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Answer 1 · 2018-01-17T09:00:57

$-3/4 <= x <= 1/4$

The domain of $sin^-1(u)$ is $-1<=u<=1$ , so for this problem we need to solve:

$-1<=2x+1/2<=1$

subtracting $1/2$ from all parts:

$-3/2 <= 2x <= 1/2$

dividing through by 2:

$-3/4 <= x <= 1/4$

What is the domain of y=3/2 arcsin(2x+.5)y=3/2 arcsin(2x+.5)?