Question

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

Answer 1

`x inRR,x!=5`
`y in RR,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 " 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`