What is the domain and range of # f(x) = 7/(x+3)#?

1 Answer
Jun 20, 2018

Answer:

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

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

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

#(-oo,-3)uu(-3,oo)larrcolor(blue)"in interval notation"#

#"let "y=7/(x+3)#

#"for range, rearrange making x the subject"#

#y(x+3)=7#

#xy+3y=7#

#xy=7-3y#

#x=(7-3y)/ytoy!=0#

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

#(-oo,0)uu(0,oo)#
graph{7/(x+3) [-10, 10, -5, 5]}