What is the domain of f(x)=(2x-4)/(14x^2-3x-5) ?

The domain of f(x)=(2x-4)/(14x^2-3x-5) is x 5/7

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domain of f(x)=(2x-4)/(14x^2-3x-5)

domain

f (x) = \frac{2 x - 4}{14 x ^{2} - 3 x - 5}

x < - \frac{1}{2} or - \frac{1}{2} < x < \frac{5}{7} or x > \frac{5}{7}

Interval Notation

(- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, \frac{5}{7}) \cup (\frac{5}{7}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{5}{7}, x = - \frac{1}{2}

The function domain

x < - \frac{1}{2} or - \frac{1}{2} < x < \frac{5}{7} or x > \frac{5}{7}

f (x) = \frac{2 x - 11}{2 x - 6}

f (x) = \frac{x ^{3} - 2 x + 4}{x - 3}

3 x - 3

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

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

What is the domain of f(x)=(2x-4)/(14x^2-3x-5) ?
The domain of f(x)=(2x-4)/(14x^2-3x-5) is x<-1/2 \lor-1/2 <x< 5/7 \lor x> 5/7