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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

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

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

x = - 1, - 2

5 sin (2 x)

\frac{4 x ^{2} - 5}{2 x ^{2} + 8}

\frac{x ^{2} + 1}{x}

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