How do you find the domain and range of #f(x)= 2/(x-5)#?

2 Answers
Jan 18, 2018

Answer:

The domain is #x in RR-{5}#. The range is #y in RR-{0}#

Explanation:

As you cannot divide by #0#, the denominator is #!=0#

#x-5!=0#, #=>#, #x!=5#

The domain is #x in RR-{5}#

To find the range, proceed as follows :

Let #y=2/(x-5)#

Rearranging

#y(x-5)=2#

#yx-5y=2#

#yx=2+5y#

#x=(2+5y)/y#

Here,

#y!=0#

The range is #y in RR-{0}#

graph{2/(x-5) [-18.02, 18.03, -9.01, 9.01]}

Jan 18, 2018

Answer:

#x inRR,x!=5#
#y inRR,y!=0#

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 "x-5=0rArrx=5larrcolor(red)"excluded value"#

#rArr"domain is "x inRR,x!=5#

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

#y=2/(x-5)#

#rArry(x-5)=2#

#rArrxy-5y=2#

#rArrxy=2+5y#

#rArrx=(5+2y)/y#

#rArry=0larrcolor(red)"is the excluded value"#

#rArr"range is "y inRR,y!=0#