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

Answer 1

Eli Assouline

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

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

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

Consequently,

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

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Answer 2

Isaiah Anthony

The domain of the function ( f(x) = \frac{2x+1}{2x-1} ) is all real numbers except ( x = \frac{1}{2} ). The range of the function is all real numbers except ( y = 1 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.