What is the domain of sqrt(-1/2+3/2 |2x-3|) ?

The domain of sqrt(-1/2+3/2 |2x-3|) is x = 5/3

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domain of sqrt(-1/2+3/2 |2x-3|)

domain

- \frac{1}{2} + \frac{3}{2} ∣ 2 x - 3 ∣

x \leq \frac{4}{3} or x \geq \frac{5}{3}

Interval Notation

(- \infty, \frac{4}{3}] \cup [\frac{5}{3}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq \frac{4}{3} or x \geq \frac{5}{3}

The function domain

x \leq \frac{4}{3} or x \geq \frac{5}{3}

What is the domain of sqrt(-1/2+3/2 |2x-3|) ?
The domain of sqrt(-1/2+3/2 |2x-3|) is x<= 4/3 \lor x>= 5/3