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

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

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

domain

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

\frac{( x + 1 )}{( x ^{2} - 13 x + 42 ) ^{\frac{1}{2}}}

f (θ) = 1 - cos (θ)

f (x) = (x - 2) + - 2 x + 5

\frac{10 x + 7}{3 - 8 x}

\frac{( x + 4 )}{( 3 x - 4 )}

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