What is the domain and range of #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#