What is the domain of f(x)=(2x)/(sqrt(12x^2-23x+5)) ?

The domain of f(x)=(2x)/(sqrt(12x^2-23x+5)) is x 5/3

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domain of f(x)=(2x)/(sqrt(12x^2-23x+5))

domain

f (x) = \frac{2 x}{12 x ^{2} - 23 x + 5}

x < \frac{1}{4} or x > \frac{5}{3}

Interval Notation

(- \infty, \frac{1}{4}) \cup (\frac{5}{3}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq \frac{1}{4} or x \geq \frac{5}{3}

Find undefined (singularity) points:

x = \frac{5}{3}, x = \frac{1}{4}

Combine real regions and undefined points for final function domain

x < \frac{1}{4} or x > \frac{5}{3}

f (x) = \frac{1}{ln ( x ^{4} - 16 )}

\frac{x}{x ^{2} - x - 2}

y = sec (x - π)

\frac{x ^{2}}{x ^{2} + 1}

\frac{1}{2} x

What is the domain of f(x)=(2x)/(sqrt(12x^2-23x+5)) ?
The domain of f(x)=(2x)/(sqrt(12x^2-23x+5)) is x< 1/4 \lor x> 5/3