How do you find the domain and range of #f(x) = (2x+1) / (2x-1)#?

1 Answer
Dec 23, 2016

Answer:

The domain is #x in RR-{1/2}#
The range is #f(x) in RR-{1}#

Explanation:

As you cannot divide by #0#, #x!=1/2#

There is a vertical asymptote #x=1/2#

Therefore,

The domain of #f(x)# is #D_(f(x))# is #x in RR-{1/2}#

#lim_(x->+-oo)f(x)=lim_(x->+-oo)(2x)/2x=1#

There is a horizontal asymptote #y=1#

The range is #f(x) in RR-{1}#

graph{(y-(2x+1)/(2x-1))(y-1)(x-1/2)=0 [-12.66, 12.65, -6.33, 6.33]}