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

The domain of f(x)=arcsin(2-4x^2) is -(sqrt(3))/2 <= x<=-1/2 \lor 1/2 <= x<= (sqrt(3))/2

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domain of f(x)=arcsin(2-4x^2)

domain

- \frac{3}{2} \leq x \leq - \frac{1}{2} or \frac{1}{2} \leq x \leq \frac{3}{2}

Interval Notation

[- \frac{3}{2}, - \frac{1}{2}] \cup [\frac{1}{2}, \frac{3}{2}]

Solution steps

Find known functions domain restrictions:

- \frac{3}{2} \leq x \leq - \frac{1}{2} or \frac{1}{2} \leq x \leq \frac{3}{2}

The function domain

- \frac{3}{2} \leq x \leq - \frac{1}{2} or \frac{1}{2} \leq x \leq \frac{3}{2}

What is the domain of f(x)=arcsin(2-4x^2) ?
The domain of f(x)=arcsin(2-4x^2) is -(sqrt(3))/2 <= x<=-1/2 \lor 1/2 <= x<= (sqrt(3))/2