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

2 Answers
Apr 4, 2017

Answer:

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]}

Apr 4, 2017

Answer:

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#