What is the domain of f(x)=(2x+3)/(3x^2+x-10) ?

The domain of f(x)=(2x+3)/(3x^2+x-10) is x 5/3

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domain of f(x)=(2x+3)/(3x^2+x-10)

domain

f (x) = \frac{2 x + 3}{3 x ^{2} + x - 10}

x < - 2 or - 2 < x < \frac{5}{3} or x > \frac{5}{3}

Interval Notation

(- \infty, - 2) \cup (- 2, \frac{5}{3}) \cup (\frac{5}{3}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{5}{3}, x = - 2

The function domain

x < - 2 or - 2 < x < \frac{5}{3} or x > \frac{5}{3}

What is the domain of f(x)=(2x+3)/(3x^2+x-10) ?
The domain of f(x)=(2x+3)/(3x^2+x-10) is x<-2\lor-2<x< 5/3 \lor x> 5/3