How do you find the domain and range of #y= x^2-2#?

1 Answer
May 13, 2017

Answer:

Domain: #x in RRcolor(white)("XXX")#or, in interval notation, #color(white)("XXX")x in (-oo,+oo)#
Range: #y in [-2,+oo)#

Explanation:

I have assumed that the Universe of Discourse is the set of Real numbers (#RR#); the answer will be a bit different if you are working in Complex (#CC#) numbers.

#x^2-2# is defined for all Real values of #x#
#rArr# the Domain is all Real values.

Since (for Real values of #x#) #x^2 >=0#
#rArr y=x^2-2 >=-2#
and
since #x^2-2 rarr +oo# as #xrarr +-oo#
#rArr y#'s upper limit is #+oo#
#rArr# the Range is #[-2,+oo)#