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]#