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

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Answer 1 · 2016-11-30T08:20:27

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

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

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]}

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