What is the domain of f(x)=(3x+1)/(2x^2-7x-4) ?

The domain of f(x)=(3x+1)/(2x^2-7x-4) is x 4

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domain of f(x)=(3x+1)/(2x^2-7x-4)

domain

f (x) = \frac{3 x + 1}{2 x ^{2} - 7 x - 4}

x < - \frac{1}{2} or - \frac{1}{2} < x < 4 or x > 4

Interval Notation

(- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 4, x = - \frac{1}{2}

The function domain

x < - \frac{1}{2} or - \frac{1}{2} < x < 4 or x > 4

What is the domain of f(x)=(3x+1)/(2x^2-7x-4) ?
The domain of f(x)=(3x+1)/(2x^2-7x-4) is x<-1/2 \lor-1/2 <x<4\lor x>4