How do you find the domain and range of #y= 1/(x+4) -1#?

1 Answer
Jun 16, 2018

Answer:

#x inRR,x!=-4,y inRR,y!=-1#

Explanation:

#"we can express y as"#

#y=1/(x+4)-(x+4)/(x+4)=(-x-3)/(x+4)#

#"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+4=0rArrx=-4larrcolor(red)"excluded value"#

#"domain "x inRR,x!=-4#

#(-oo,-4)uu(-4,oo)larrcolor(blue)"in interval notation"#

#"to find range rearrange making x the subject"#

#y(x+4)=-x-3#

#xy+4y=-x-3#

#xy+x=-3-4y#

#x(y+1)=-(3+4y)#

#x=-(3+4y)/(y+1)#

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

#"range "y inRR,y!=-1#

#(-oo,-1)uu(-1,oo)larrcolor(blue)"in interval notation"#
graph{1/(x+4)-1 [-10, 10, -5, 5]}