# How do you find the domain and range of #f(x) = 7 / (2x-10)#?

##### 1 Answer

Apr 7, 2017

#### 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 " 2x-10=0rArrx=5larrcolor(red)" value that x cannot be"#

#rArr"domain is " x in RR,x!=5#

#"Rearrange f(x) making x the subject"#

#y=7/(2x-10)#

#rArry(2x-10)=7#

#rArr2xy-10y=7#

#rArr2xy=7+10y#

#rArrx=(7+10y)/(2y)#

#"Apply the same reasoning as for domain"#

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