Precalculus Examples

$f (x) = \cos^{-1} (x)$

Step 1

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

$x \geq - 1$

Step 2

Set the argument in $\cos^{-1} (x)$ 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:

$[0, π]$

Set-Builder Notation:

${y | 0 \leq y \leq π}$

Step 5

Determine the domain and range.

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

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

Step 6