What is the domain of f(x)=arccos(sqrt(-2x^2+3)) ?

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

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domain of f(x)=arccos(sqrt(-2x^2+3))

domain

f (x) = arccos (- 2 x^{2} + 3)

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

Interval Notation

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

Solution steps

Find known functions domain restrictions:

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

The function domain

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

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

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

- \frac{1}{x + 3}

f (x) = \frac{x ( x + 8 )}{9 ( x - 5 )}

f (x) = \frac{- 1}{x + 2}

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