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How do you find the domain of #f(x)=1/(x-3)#?

Answer 1

#x #= R -{3}

Domain of a function means selecting the values which makes the domain defined. In this case, If the denominator is zero then the function is not defined, So for what value of #x# will the denominator be 0 ?

3 is correct?

when #x# = 3 ,

#f(x) = 1/0 # which is not defined.

Your function is legitimate even if you maintain any other values besides 3.

Thus, the domain consists of all real line values other than 3.

#x #= R -{3}

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Answer 2

Avery Alexander

To find the domain of the function (f(x) = \frac{1}{x-3}), we need to determine all the values of (x) for which the function is defined. The function is undefined when the denominator is zero because division by zero is undefined. So, we set the denominator equal to zero and solve for (x).

(x - 3 = 0)

(x = 3)

Therefore, the domain of the function (f(x) = \frac{1}{x-3}) is all real numbers except (x = 3). So, the domain is (x \in \mathbb{R} - {3}).

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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.