# What is the domain and range of y = arccos({x-4}/{8})?

Aug 24, 2016

Domain$= \left[- 4 , 12\right]$, and,

Range$= \left[0 , \pi\right]$.

#### Explanation:

Let us recall the Defn. of $a r c \cos$ function :

$a r c \cos t = \theta , | t | \le 1 , \iff \cos \theta = t , \theta \in \left[0 , \pi\right]$

Hence, the Domain for the given function, is, given by,

$| \frac{x - 4}{8} | \le 1 \Rightarrow | x - 4 | \le 8 \Rightarrow 4 - 8 \le x \le 4 + 8 ,$ i.e.,

$- 4 \le x \le 12 , \mathmr{and} , x \in \left[- 4 , 12\right]$

The Range is $y \in \left[0 , \pi\right]$