What is the domain of arccos(2x)*ln(x^2) ?

The domain of arccos(2x)*ln(x^2) is -1/2 <= x<0\lor 0<x<= 1/2

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domain of arccos(2x)*ln(x^2)

domain

arccos (2 x) \cdot ln (x^{2})

- \frac{1}{2} \leq x < 0 or 0 < x \leq \frac{1}{2}

Interval Notation

[- \frac{1}{2}, 0) \cup (0, \frac{1}{2}]

Solution steps

Find positive values for logs:

x < 0 or x > 0

Find known functions domain restrictions:

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

Combine real regions and undefined points for final function domain

- \frac{1}{2} \leq x < 0 or 0 < x \leq \frac{1}{2}

f (x) = \frac{2}{x ^{2} + 2 x - 24}

\frac{( x ^{2} - 2 x )}{x ^{2} + x - 6}

f (x) = \frac{- 3 - 5 y}{3 y - 4}

f (x) = \frac{5 x + 18}{x ^{2} + 5 x - 6}

f (x) = \frac{4 x ^{2} + 23 x - 56}{x ^{2} - 4 x - 32}

What is the domain of arccos(2x)*ln(x^2) ?
The domain of arccos(2x)*ln(x^2) is -1/2 <= x<0\lor 0<x<= 1/2