What is the domain of f(x)= 1/(6x^2-x-15) ?

The domain of f(x)= 1/(6x^2-x-15) is x 5/3

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domain of f(x)= 1/(6x^2-x-15)

domain

f (x) = \frac{1}{6 x ^{2} - x - 15}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

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

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

f (x) = x^{2} - 3 x + 1

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

f (x) = \frac{x + 9}{( x + 4 ) ( x - 8 )}

What is the domain of f(x)= 1/(6x^2-x-15) ?
The domain of f(x)= 1/(6x^2-x-15) is x<-3/2 \lor-3/2 <x< 5/3 \lor x> 5/3