How do you find the domain and range of #f(x)= (x+7)/(2x-8)#?

1 Answer
Jul 24, 2018

Answer:

#x inRR,x!=4,y inRR,y!=1/2#

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 "2x-8=0rArrx=4larrcolor(red)"excluded value"#

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

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

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

#"let "y=(x+7)/(2x-8)#

#y(2x-8)=x+7#

#2xy-8y=x+7#

#2xy-x=7+8y#

#x(2y-1)=7+8y#

#x=(7+8y)/(2y-1)#

#"solve "2y-1=0rArry=1/2larrcolor(red)"excluded value"#

#"range is "y inRR,y!=1/2#

#(-oo,1/2)uu(1/2,+oo)#
graph{(x+7)/(2x-8) [-10, 10, -5, 5]}