Find the Domain and Range y=2arcsin(x)

$y = 2 \arcsin (x)$

Step 1

Set the argument in $\arcsin (x)$ greater than or equal to $- 1$ to find where the expression is defined.

$x \geq - 1$

Step 2

Set the argument in $\arcsin (x)$ less than or equal to $1$ to find where the expression is defined.

$x \leq 1$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[- 1, 1]$

Set-Builder Notation:

${x | - 1 \leq x \leq 1}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$[- π, π]$

Set-Builder Notation:

${y | - π \leq y \leq π}$

Step 5

Determine the domain and range.

Domain: $[- 1, 1], {x | - 1 \leq x \leq 1}$

Range: $[- π, π], {y | - π \leq y \leq π}$

Step 6