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

1 Answer
Apr 15, 2016

Answer:

Domain: all Real values excluding #1#
Range: all Real values excluding #0#

Explanation:

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

Since division by #0# is undefined
#color(white)("XXX")x-1 != 0#
#color(white)("XXX")rarr x != 1#
However #f(x)# is defined for all other values of #x#

Since #f(x)=1/(x-1)#
then
#color(white)("XXX")(x-1)*f(x)=1#
and the question of "Range" becomes
#color(white)("XXX")#for what value(s) of #f(x)# is this not possible.
The only answer is that it is not possible if #f(x)=0#.
So the Range is all Real values except #0#