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

1 Answer
Aug 26, 2017

Answer:

#x inRR,x!=-3#
#y inRR,y!=0#

Explanation:

#"given "y=1/(x+3)#

#"the denominator 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+3=0rArrx=-3larrcolor(red)" excluded value"#

#rArr"domain is "x inRR,x!=-3#

#"to find any excluded values in the range rearrange"#
#"making x the subject"#

#rArry(x+3)=1larrcolor(blue)" cross-multiplying"#

#rArrxy+3y=1#

#rArrxy=1-3y#

#rArrx=(1-3y)/y#

#"the denominator cannot be zero"#

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

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