What is the domain of f(x)=(x-3)/(2x^2+x-21) ?

The domain of f(x)=(x-3)/(2x^2+x-21) is x 3

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domain of f(x)=(x-3)/(2x^2+x-21)

domain

x < - \frac{7}{2} or - \frac{7}{2} < x < 3 or x > 3

Interval Notation

(- \infty, - \frac{7}{2}) \cup (- \frac{7}{2}, 3) \cup (3, \infty)

Solution steps

Find undefined (singularity) points:

x = 3, x = - \frac{7}{2}

The function domain

x < - \frac{7}{2} or - \frac{7}{2} < x < 3 or x > 3

What is the domain of f(x)=(x-3)/(2x^2+x-21) ?
The domain of f(x)=(x-3)/(2x^2+x-21) is x<-7/2 \lor-7/2 <x<3\lor x>3