How do you find the domain and range of #f(x) = 1/x#?

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Answer 1 · 2018-06-09T20:17:54

Domain: #{x|x in RR:x!=0}#
Domain interval notation #(-oo,0)uu(0,oo)#

Range: #{f(x)|f(x) in RR}#
Range interval notation #(-oo,oo)#

The only value in the domain excluded is when the function is undefined: #1/0#, that is when #x=0#

Domain: #{x|x in RR:x!=0}# in interval notation #(-oo,0)uu(0,oo)#

Now for the range, the function #f(x)=1/x# is continuous across the domain above.

#x -> +-oo, f(x) ->0#

#x -> 4^+, f(x) -> oo#

#x -> 4^-, f(x) -> -oo#

so the range is:

Range : #{f(x)|f(x) in RR}# or in interval notation #(-oo,oo)#

graph{1/x [-10, 10, -5, 5]}