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

$y = \arccos (x - 2)$

Set the argument in $\arccos (x - 2)$ greater than or equal to $- 1$ to find where the expression is defined.

$x - 2 \geq - 1$

Move all terms not containing $x$ to the right side of the inequality.

Add $2$ to both sides of the inequality.

$x \geq - 1 + 2$

Add $- 1$ and $2$ .

$x \geq 1$

Set the argument in $\arccos (x - 2)$ less than or equal to $1$ to find where the expression is defined.

$x - 2 \leq 1$

Move all terms not containing $x$ to the right side of the inequality.

Add $2$ to both sides of the inequality.

$x \leq 1 + 2$

Add $1$ and $2$ .

$x \leq 3$

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

Interval Notation:

$[1, 3]$

Set-Builder Notation:

${x | 1 \leq x \leq 3}$

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

Interval Notation:

$[0, π]$

Set-Builder Notation:

${y | 0 \leq y \leq π}$

Determine the domain and range.

Domain: $[1, 3], {x | 1 \leq x \leq 3}$

Range: $[0, π], {y | 0 \leq y \leq π}$