How do you find the domain and range of #f(x)=1/x+3 #?

1 Answer
Apr 15, 2017

Answer:

#x inRR,x!=0#
#y inRR,y!=3#

Explanation:

You may wish to consider f(x) as a single rational function.

#f(x)=1/x+3=1/x+(3/1xx x/x)=1/x+(3x)/x#

#rArry=f(x)=(1+3x)/x#

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.

#rArrx=0larrcolor(red)" excluded value in domain"#

#"domain is " x inRR,x!=0#

#"Rearrange f(x) to make x the subject"#

#y=(1+3x)/x#

#rArrxy=1+3x#

#rArrxy-3x=1#

#rArrx(y-3)=1#

#rArrx=1/(y-3)to(y!=3)color(red)" excluded value in range"#

#"range is " y inRR,y!=3#