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

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

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

domain

f (x) = \frac{3 x ^{2} + 7 x - 1}{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{7 x ^{2} - 8 x + 11}{x - 6}

f (x) = 4^{x + 2}

g (x) = 2^{x} + 2

\frac{1}{sin ( x )}

f (x) = x^{2} - 10 ln (x)

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