What is the domain of f(x)=(3x^2-21x)/(6x^2-39x-21) ?

The domain of f(x)=(3x^2-21x)/(6x^2-39x-21) is x 7

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domain of f(x)=(3x^2-21x)/(6x^2-39x-21)

domain

f (x) = \frac{3 x ^{2} - 21 x}{6 x ^{2} - 39 x - 21}

x < - \frac{1}{2} or - \frac{1}{2} < x < 7 or x > 7

Interval Notation

(- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, 7) \cup (7, \infty)

Solution steps

Find undefined (singularity) points:

x = 7, x = - \frac{1}{2}

The function domain

x < - \frac{1}{2} or - \frac{1}{2} < x < 7 or x > 7

- 2 x^{4} + 5 x^{2}

f (x) = \frac{1}{5} (x) - 6

f (x) = \frac{x - 4}{x ^{2} + 8 x - 20}

\frac{3 x ^{2} - 11 x - 4}{x - 4}

lo g_{10} (∣ 4 x + 8 ∣)

What is the domain of f(x)=(3x^2-21x)/(6x^2-39x-21) ?
The domain of f(x)=(3x^2-21x)/(6x^2-39x-21) is x<-1/2 \lor-1/2 <x<7\lor x>7