What is the domain and range of #F(x)=(x+2) /( x-2)#?

1 Answer
Jul 4, 2017

Answer:

#x inRR,x!=2#
#y inRR,y!=1#

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-2=0rArrx=2larrcolor(red)" excluded value"#

#rArr"domain is " x inRR,x!=2#

To find any excluded value in the range rearrange f(x) making x the subject.

#y=(x+2)/(x-2)#

#rArry(x-2)=x+2larrcolor(blue)" cross multiplying"#

#rArrxy-2y=x+2larrcolor(blue)" distributing"#

#rArrxy-x=2+2ylarrcolor(blue)" collecting terms in x"#

#rArrx(y-1)=2+2ylarrcolor(blue)" factoring"#

#rArrx=(2+2y)/(y-1)#

#"the denominator cannot equal zero"#

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

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