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

1 Answer
Jun 9, 2017

Answer:

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

Explanation:

#"the denominator of y cannot be zero as this would make y"#
#color(blue)"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 the"#
#"function making x the subject"#

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

#rArrxy+5y=x#

#rArrxy-x=-5y#

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

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

#"the denominator cannot be zero"#

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

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