Question

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

Answer 1

`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`