What is the domain of f(x)=(6x^2+x-5)/(3x^2-7x-20) ?

The domain of f(x)=(6x^2+x-5)/(3x^2-7x-20) is x 4

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domain of f(x)=(6x^2+x-5)/(3x^2-7x-20)

domain

f (x) = \frac{6 x ^{2} + x - 5}{3 x ^{2} - 7 x - 20}

x < - \frac{5}{3} or - \frac{5}{3} < x < 4 or x > 4

Interval Notation

(- \infty, - \frac{5}{3}) \cup (- \frac{5}{3}, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 4, x = - \frac{5}{3}

The function domain

x < - \frac{5}{3} or - \frac{5}{3} < x < 4 or x > 4

What is the domain of f(x)=(6x^2+x-5)/(3x^2-7x-20) ?
The domain of f(x)=(6x^2+x-5)/(3x^2-7x-20) is x<-5/3 \lor-5/3 <x<4\lor x>4