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How do you find the domain of #f(x) = (x+3)/(2x-5)#?

Answer 1

The domain is the set of all the #x-#values.
#x epsilon RR, x != -5/2#

We have to decide if there are any values of #x# which are invalid.

Looking at the numerator, #x + 3#, there is no problem or restriction for a value of #x#. The numerator can even be equal to 0

However, the denominator of a fraction may not be equal to 0. If #2x+ 5 =0#, then the value of #x# is #-5/2#

So, for the domain, #x epsilon RR, x != -5/2#

This reads as "#x# may be any real number except #-5/2#.

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Answer 2

Eli Assouline

The domain of f(x) = (x + 3)/(2x - 5) is all real numbers except x = 2.5 (because the denominator cannot be zero).

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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.