What is the domain and range of $f (x) = \frac{x - 2}{x^{2} - 6 x + 9}$ $f(x)=(x-2)/(x^2-6x+9)$ ?

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Answer 1 · 2017-01-23T07:55:51

The domain of $=RR-{3}$
The range of $=RR$

Let's factorise the denominator

$x^2-6x+9=(x-3)^2$

As you cannot divide by $0$ , $x!=3$

The domain of $f(x)$ is $D_f(x)=RR-{3}$

$lim_(x->-oo)f(x)=lim_(x->-oo)x/x^2=lim_(x->-oo)1/x=0^-$

$lim_(x->+oo)f(x)=lim_(x->+oo)x/x^2=lim_(x->+oo)1/x=0^+$

$f(0)=-2/9$

What is the domain and range of f(x)=(x-2)/(x^2-6x+9)f(x)=x−2x2−6x+9f(x)=(x-2)/(x^2-6x+9)?