What is the domain and range of # f(x) = sqrt(x^2-36)#?

1 Answer
Dec 19, 2015

Answer:

Domain: #RR, (-oo,-6] uu [+6,+oo]#
Range: #RR, [0,+oo)#

Explanation:

#f(x)# is defined in the Real numbers provided
#color(white)("XXX")x^2-36 >= 0#
This will be true provided
#color(white)("XXX")x >= 6color(white)("XX")#or#color(white)("XX")x <=-6#
Therefore the domain (in #RR#) is #x in (+oo,-6]uu[+6,+oo)#

Since #sqrt("any real number")# is defined as the principle square root (i.e. #>= 0)#
the range is #f(x) in [0,+oo)#