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# find the domain: f(x)= (x-3)/(x-4)?

I know the answer is (-∞,4)U(4,∞) but I don't understand how to get to that answer. Can someone explain how to find the domain?

### 6 Answers

- MyRankLv 64 weeks ago
f(x) = (x-3)/(x-4)

x-4 = 0

x = 4

now domain is x ≠ 4

∴ xϵ(-∞, ∞) – {4}

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- Engr. RonaldLv 74 weeks ago
We equate the denominator of f(x) = (x - 3)/(x - 4) equal to zero to get its domain.

our denominator is x - 4

so

x - 4 = 0

x = 4

so our domain is x≠ 4

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- Iggy RockoLv 74 weeks ago
The domain is all numbers except x = 4 because that leads to the denominator equaling 0.

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- ?Lv 74 weeks ago
Given

..........x-3

f(x) = -----

..........x-4

Looking at the numerator: there is no restriction on x.

Looking at the denominator:

We know that fractions are undefined if the denominator equals 0, so for f(x) to be defined, x-4 ≠ 0 or x ≠ 4.

So the restrictions for f(x) are simply that x≠4.

Therefore, the domain of f(x) is (-∞,4)U(4,∞)..................ANS

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- Barkley HoundLv 74 weeks ago
x can be any number other than 4 since 4-4=0 and you can not divide by 0.

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- AlanLv 74 weeks ago
Since you don't have even roots (square roots, x^(1/4) , or log values)

the only restrictions are where you divide by zero

so the only restriction is when the denominator = 0

so when x -4 = 0

so when x = 4 , you divide by zero and it is you only restriction

x cannot equal 4

in interval notation , the

domain becomes

(-∞,4)U(4,∞)

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