What is the domain of g(x)= x/(4x^2-9) ?

The domain of g(x)= x/(4x^2-9) is x 3/2

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domain of g(x)= x/(4x^2-9)

domain

g (x) = \frac{x}{4 x ^{2} - 9}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

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

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

f (x) = 2 tan (2 x) + 1

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

f (x) = \frac{x - a}{x + π}

f (x) = \frac{4}{5} x

What is the domain of g(x)= x/(4x^2-9) ?
The domain of g(x)= x/(4x^2-9) is x<-3/2 \lor-3/2 <x< 3/2 \lor x> 3/2