Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

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

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  • MyRank
    Lv 6
    4 weeks ago

    f(x) = (x-3)/(x-4)

    x-4 = 0

    x = 4

    now domain is x ≠ 4

    ∴ xϵ(-∞, ∞) – {4}

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  • 4 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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  • 4 weeks ago

    The domain is all numbers except x = 4 because that leads to the denominator equaling 0.

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  • ?
    Lv 7
    4 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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  • 4 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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  • Alan
    Lv 7
    4 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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