How do you find the domain and range of #y= .5cos(x/2-2sqrt3)+1#?

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Answer 1 · 2017-09-10T06:30:15

The domain is #x in RR#
The range is # y in [0.5, 1.5]#

By definition, cosine is defined over #RR#

so, the domain is #=RR#

The range of cosine is

#-1<= cos(x/2-2sqrt3)<=1#

Multiply by #0.5#

#-1*0.5<= 0.5*cos(x/2-2sqrt3)<=1*0.5#

#-0.5<= 0.5*cos(x/2-2sqrt3)<=0.5#

Add #1#

#-0.5+1<= 0.5*cos(x/2-2sqrt3)+1<=0.5+1#

#+0.5<= 0.5*cos(x/2-2sqrt3)+1<=1.5#

#+0.5<= y <=1.5#