How do you find the domain and range of #3-cos2x#?

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Answer 1 · 2017-08-05T13:22:48

Domain:# (-oo, +oo)#
Range: # [4,2]#

#f(x) = 3-cos2x#

#f(x)# is defined #forall x in RR#

Hence, the domain of #f(x) = (-oo, +oo)#

Let #theta =2x#

#:. f(x) = 3-costheta#

The range of #cos theta =+-1#

#:.# the range of #f(x) = [3+1, 3-1] = [4,2]#

This can be see from the graph of #f(x)# below.

graph{3-cos(2x) [-10.21, 9.79, -1.76, 8.24]}