How do you find the domain and range of #f(x)=3/(x-1)#?

1 Answer
Jim G.
May 9, 2017

#x inRR,x!=1#

#y inRR,y!=0#

Explanation:

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

#"solve" x-1=0rArrx=1larrcolor(red)" excluded value"#

#"domain is " x inRR,x!=1#

#"to find any excluded values for y"#

#"rearrange f(x), making x the subject"#

#y=3/(x-1)#

#rArry(x-1)=3#

#rArrxy-y=3#

#rArrx=(3+y)/y#

#"the denominator cannot be zero"#

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

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

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