Precalculus Examples

$f (x) = \cos (\arccos (x))$

Step 1

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

$x \geq - 1$

Step 2

Set the argument in $\arccos (x)$ 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