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

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}

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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