How do you find the domain and range of f(x) = (x-2)/(x+1)?
1 Answer
Jan 29, 2018
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]}
