How do you find the domain and range of #f(x)=2/(x-1)#?

1 Answer
Jul 13, 2018

Answer:

The domain is #x in (-oo,1) uu(1,+oo)#. The range is #y in (-oo,0)uu(0,+oo)#.

Explanation:

The function is

#f(x)=2/(x-1)#

As we cannot divide by #0#, the denominator must be #!=0#

#x-1!=0#

#x!=1#

The domain is #x in (-oo,1) uu(1,+oo)#

To find the range, let

#y=2/(x-1)#

#y(x-1)=2#

#yx-y=2#

#yx=2+y#

#x=(2+y)/y#

As we cannot divide by #0#, the denominator must be #!=0#

#y!=0#

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

graph{2/(x-1) [-12.66, 12.65, -6.33, 6.33]}