How do you find the domain and range of # 1/(x-7)#?

1 Answer
Jim G.
Apr 12, 2017

#x inRR,x!=7#
#y inRR,y!=0#

Explanation:

#"let " y=1/(x-7)#

The denominator of y cannot equal zero as tis would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve " x-7=0rArrx=7larrcolor(red)" excluded value"#

#rArr" domain is " x inRR,x!=7#

#"Rearrange the function to make x the subject"#

#rArry(x-7)=1#

#rArrxy-7y=1#

#rArrxy=1+7y#

#rArrx=(1+7y)/y#

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

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

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