How do you find the domain and range of #f(x)=5/(x-3)#?

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Answer 1 · 2018-05-20T17:13:16

The domain is #x in (-oo,3)uu(3,+oo)#. The range is #y in (-oo,0)uu(0,+oo)#

The denominator must be #!=0#

Therefore,

#x-3!=#

#=>#, #x!=3#

The domain is #x in (-oo,3)uu(3,+oo)#

To find the range, proceed as follows :

Let #y=5/(x-3)#

#y(x-3)=5#

#yx-3y=5#

#yx=5+3y#

#x=(5+3y)/(y)#

The denominator is #!=0#

#y!=0#

The range is #y in (-oo,0)uu(0,+oo)#

graph{5/(x-3) [-18.02, 18.02, -9.01, 9.02]}