# For #f(x) = 1/(x-3)#, what is the natural domain and range?

##### 1 Answer

Mar 9, 2018

#### 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-3=0rArrx=3larrcolor(red)"excluded value"#

#"domain is "x inRR,x!=3#

#(-oo,3)uu(3,+oo)larrcolor(blue)"in interval notation"#

#"to find the range, rearrange making x the subject"#

#f(x)=y=1/(x-3)#

#rArry(x-3)=1#

#rArrxy-3y=1#

#rArrxy=1+3y#

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

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

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

#(-oo,0)uu(0,+oo)larrcolor(blue)"in interval notation"#

graph{1/(x-3) [-10, 10, -5, 5]}