How do you find the domain and range of #y = { x/ (x + 5) }#?

1 Answer
Aug 19, 2017

Answer:

#x inRR,x!=-5#
#y inRR,y!=1#

Explanation:

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

#"solve "x+5=0rArrx=-5larrcolor(red)" excluded value"#

#rArr"domain is "x inRR,x!=-5#

To find any excluded values in the range rearrange making x the subject.

#rArry(x+5)=xlarrcolor(blue)" cross-multipling"#

#rArrxy+5y=x#

#rArrxy-x=-5ylarrcolor(blue)" collect term in x together"#

#rArrx(y-1)=-5ylarrcolor(blue)" factor out x"#

#rArrx=-5y/(y-1)#

#"the denominator cannot equal zero"#

#"solve "y-1=0rArry=1larrcolor(red)" excluded value"#

#rArr"range is "y inRR,y!=1#