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

The domain of f(x)=(3+|x|)/(2x^2+5x-3) is x 1/2

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domain of f(x)=(3+|x|)/(2x^2+5x-3)

domain

f (x) = \frac{3 + ∣ x ∣}{2 x ^{2} + 5 x - 3}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

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

f (x) = - x^{2} + 3

\frac{4 x ^{2}}{x ^{2} + 4}

y = \frac{3}{4} x, (20, 15)

y = 4 - \frac{1}{2 x + 1}

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