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How do you find the domain of #f(x)=3/(x-4)#?

Answer 1

Eva Abramson

In order for #f(x)# to be defined you need the denominator not equal to zero.

Hence #D_f=R-{4}# where #R# is the set of real numbers

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Answer 2

Nathan Axel

To find the domain of the function ( f(x) = \frac{3}{x-4} ), we need to identify any values of ( x ) that would result in division by zero. In this case, the function is undefined when ( x = 4 ), because division by zero is not allowed in mathematics. Therefore, the domain of the function is all real numbers except ( x = 4 ), which can be expressed as:

[ \text{Domain} = { x \in \mathbb{R} : x \neq 4 } ]

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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.