How do you find the domain and range of #f(x) = (x-2)/(x+1)#?

1 Answer
Jan 29, 2018

Answer:

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

Explanation:

The denominator of f(x) cannot be zero as tis would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve "x+1=0rArrx=-1larrcolor(red)"excluded value"#

#"domain is "x inRR,x!=-1#

#(-oo,-1)uu(-1,+oo)larrcolor(blue)"in interval notation"#

#"divide terms on numerator/denominator by x"#

#f(x)=(x/x-2/x)/(x/x+1/x)=(1-2/x)/(1+1/x)#

#"as "xto+-oo,f(x)to(1-0)/(1+0)#

#rArry=1larrcolor(red)"excluded value"#

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

#(-oo,1)uu(1,+oo)larrcolor(blue)"in interval notation"#
graph{(x-2)/(x+1) [-10, 10, -5, 5]}