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

1 Answer
May 16, 2017

Answer:

#x inRR,x!=-2#
#y inRR,y!=1#

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) #color(blue)"undefined".#Eqating the denominator to zero and solving gives the value that x cannot be.

#"solve " x+2=0rArrx=-2larrcolor(red)" excluded value"#

#rArr"domain is " x inRR,x!=-2#

#"to find any excluded values in the range"#

#"rearrange f(x) = y making x the subject"#

#rArry=(x+4)/(x+2)larr" cross-multiply"#

#rArry(x+2)=x+4#

#rArrxy+2y-x=4#

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

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

#"the denominator cannot be zero"#

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

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