What is the domain of f(x)=sqrt(x^2-1/4) ?

The domain of f(x)=sqrt(x^2-1/4) is x = 1/2

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domain of f(x)=sqrt(x^2-1/4)

domain

f (x) = x^{2} - \frac{1}{4}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

The function domain

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

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