How do you find the domain and range of #y = 1/(x^2 - 2)#?

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Answer 1 · 2017-11-15T01:55:48

Domain = #{x in RR|x != +-sqrt2}#
Range = #{y in RR | y != 0}#

This will be undefined where the denominator is 0:

#x^2-2=0#
#(x-sqrt2)(x+sqrt2) = 0#
#x = +-sqrt2#

So the domain will consist of all points where x doesn't equal #+-sqrt2#

Domain = #{x in RR|x != +-sqrt2}#

Since the denominator has a higher degree than the numerator, the rational equation has a horizontal asymptote at y = 0.

This means the range will consist of all points where y doesn't equal 0

Range = #{y in RR | y != 0}#