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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

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

f (x) = x^{2} lo g_{e} (x)

f (x) = (14 x^{(3)}) - 13

f (x) = \frac{1}{x + 3}

f (x) = - 3 sin (x - \frac{π}{4}) + 2

f (x) = \frac{3 x - 5}{x}

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