Find Domain of Rational Function?

Find domain of rational function.

R(x) = 3(x^2 - x - 6)/4(x^2 - 9)

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  • mizoo
    Lv 7
    9 months ago
    Favorite Answer

    R(x) = 3(x^2 - x - 6)/[4(x^2 - 9)]

    x^2 - 9 ≠ 0

    x ≠ ±3

    Domain: R - {-3, 3}

    R(x) = 3(x^2 - x - 6)/[4(x^2 - 9)]

    R(x) = 3(x - 3)(x + 2)/[4(x - 3)(x + 3)]

    R(x) = 3(x + 2)/[4(x + 3)]

    lim x→∞, R(x) = 3/4

    Range: R - {3/4}

  • DWRead
    Lv 7
    9 months ago

    I'm assuming you mean R(x) = 3(x²-x-6)/(4(x²-9)).

    4(x²-9) ≠ 0

    x²-9 ≠ 0

    x² = 9

    x = ±3

    domain in interval notation: (-∞,-3) U (-3,3) U (3,∞)

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  • 9 months ago

    x can be any real number except 3 or -3.

    When x is quite NEAR 3, the function value is quite near 5/8; when x is near -3, the function value grows without bound.

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