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

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Answer 1 · 2016-08-24T05:27:46

Domain $=[-4,12]$ , and,

Range $=[0,pi]$ .

Let us recall the Defn. of $arc cos$ function :

$arc cost=theta, |t|<=1, iff costheta=t, theta in [0,pi]$

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

$|(x-4)/8|<=1 rArr |x-4|<=8 rArr 4-8<=x<=4+8,$ i.e.,

$-4<=x<=12, or, x in [-4,12]$

The Range is $y in [0,pi]$

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