How do you find domain and range for #f(x)=(x-2)/(x+4) #?

1 Answer
Jun 25, 2018

Answer:

#x inRR,x!=-4,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+4=0rArrx=-4larrcolor(red)"excluded value"#

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

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

#"let "y=(x-2)/(x+4)#

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

#y(x+4)=x-2#

#xy+4y=x-2#

#xy-x=-2-4y#

#x(y-1)=-2-4y#

#x=(-2-4y)/(y-1)#

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

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

#"or "(-oo,1)uu(1,oo)#
graph{(x-2)/(x+4) [-10, 10, -5, 5]}