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

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

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

domain

f (x) = \frac{x - 2}{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) = - x^{3} + 10 x^{2} + x - 3

f (x) = \frac{1}{3} x + 4

f (x) = lo g_{10} (4) (5 x - 9)

\frac{5}{( x + 6 ) + 5}

(x + 14)^{2} - 14

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