What is the domain of f(x)=(arcsin(2x))/(arccos(2x)) ?

The domain of f(x)=(arcsin(2x))/(arccos(2x)) is -1/2 <= x< 1/2

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domain of f(x)=(arcsin(2x))/(arccos(2x))

domain

f (x) = \frac{arcsin ( 2 x )}{arccos ( 2 x )}

- \frac{1}{2} \leq x < \frac{1}{2}

Interval Notation

[- \frac{1}{2}, \frac{1}{2})

Solution steps

Find known functions domain restrictions:

- \frac{1}{2} \leq x \leq \frac{1}{2}

Find undefined (singularity) points:

x = \frac{1}{2}

Combine real regions and undefined points for final function domain

- \frac{1}{2} \leq x < \frac{1}{2}

f (x) = \frac{x}{x ^{2} - 16}

\frac{4 x + 3}{2 x + 2}

\frac{3}{( \frac{5}{x - 1} ) + 4}

y = x^{3} + 3 x^{2}

f (x) = 4 x^{5} + 16 x^{2} + 8

What is the domain of f(x)=(arcsin(2x))/(arccos(2x)) ?
The domain of f(x)=(arcsin(2x))/(arccos(2x)) is -1/2 <= x< 1/2