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

1 Answer
Nov 30, 2016

The domain is #x in ] -oo,1 [ uu ] 1,+oo[ #

The range is #f(x) in ] -oo,1 [ uu ] 1,+oo [ #

Explanation:

As you cannot divide by #0#, #x!=1#

So the domain is #x in ] -oo,1 [ uu ] 1,+oo[ #

For the limits #x->+-oo#, we take the terms of highest degree in the numerator and the deniminator

#lim_(x->+-oo)f(x)=lim_(x->+-oo)x/x=1#

#lim_(x->1^(-))f(x)=1/0^(-)=-oo#

#lim_(x->1^(+))f(x)=1/0^(+)=+oo#

So the range is #f(x) in ] -oo,1 [ uu ] 1,+oo [ #

graph{x/(x-1) [-10, 10, -5, 4.995]}