What is the domain of f(x)=(4x(x-6))/(2x^2-5x-3) ?

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

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domain of f(x)=(4x(x-6))/(2x^2-5x-3)

domain

x < - \frac{1}{2} or - \frac{1}{2} < x < 3 or x > 3

Interval Notation

(- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, 3) \cup (3, \infty)

Solution steps

Find undefined (singularity) points:

x = 3, x = - \frac{1}{2}

The function domain

x < - \frac{1}{2} or - \frac{1}{2} < x < 3 or x > 3

What is the domain of f(x)=(4x(x-6))/(2x^2-5x-3) ?
The domain of f(x)=(4x(x-6))/(2x^2-5x-3) is x<-1/2 \lor-1/2 <x<3\lor x>3