How do you find the domain and range of #f(x) = 5/(x-9)#?

1 Answer
Jim G.
Dec 28, 2017

#x inRR,x!=9#
#y inRR,y!=0#

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve "x=9=0rArrx=9larrcolor(red)"excluded value"#

#rArr"domain is "x inRR,x!=9#

#"for the range rearrange making x the subject"#

#y=5/(x-9)#

#"multiply both sides by "(x-9)#

#rArry(x-9)=5#

#rArrxy-9y=5#

#rArrxy=5+9y#

#rArrx=(5+9y)/y#

#"the denominator cannot equal zero"#

#rArry=0larrcolor(red)"excluded value"#

#rArr"range is "y inRR,y!=0#

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