Question

How do you find the domain and range of `y = 1 / (x+5)`?

Answer 1

Domain is `{x in RR ; x != -5 }`
Range is `{y in RR ; y != 0 }`

Explanation:

Domain: Denominator should not be `0 :. x+5 != 0 or x != -5`
Domain is any real value except `x = -5` or `{x in RR ; x != -5 }`

Range is any real value except `y = 0` or `{y in RR ; y != 0 }` graph{1/(x+5) [-10, 10, -5, 5]}

Answer 2

see explanation.

Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

`"solve " x+5=0rArrx=-5`

`rArr"domain is " x in RR,x!=-5`

`"Rearrange "y " to make x the subject"`

`y(x+5)=1`

`rArrxy+5y=1rArrxy=1-5y`

`rArrx=(1-5y)/y`

Applying the same reasoning as for the domain we obtain.

`"range is " y in RR,y!=0`