Find the Domain and Range y=arccos(x)-2

$y = \arccos (x) - 2$

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

$x \geq - 1$

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

$x \leq 1$

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

Interval Notation:

$[- 1, 1]$

Set-Builder Notation:

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

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

Interval Notation:

$[- 2, π - 2]$

Set-Builder Notation:

${y | - 2 \leq y \leq π - 2}$

Determine the domain and range.

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

Range: $[- 2, π - 2], {y | - 2 \leq y \leq π - 2}$