What is the domain and range of #f(x)=2sin(x+pi)-4#?

1 Answer
Dec 24, 2015

Answer:

Domain: #RR#
Range: #[-6,-2] in RR#

Explanation:

#sin(x+pi)# is defined for all Real values of #x#
therefore #2sin(x+pi)-4# is defined for all real values of #x#
#rArr# Domain #= RR#

#sin(theta)# for all #theta in RR# (including #theta=x+pi#) has a Range of #[-1,+1]#
therefore #2sin(x+pi)# has a Range of #[-2,+2]#
and
#2sin(x+pi)-4# has a Range of #[-2-4,+2-4] = [-6,-2]# (in #RR#)