What is the domain of f(x)=sqrt(12x^2-5x-150) ?

The domain of f(x)=sqrt(12x^2-5x-150) is x = 15/4

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domain of f(x)=sqrt(12x^2-5x-150)

domain

x \leq - \frac{10}{3} or x \geq \frac{15}{4}

Interval Notation

(- \infty, - \frac{10}{3}] \cup [\frac{15}{4}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{10}{3} or x \geq \frac{15}{4}

The function domain

x \leq - \frac{10}{3} or x \geq \frac{15}{4}

What is the domain of f(x)=sqrt(12x^2-5x-150) ?
The domain of f(x)=sqrt(12x^2-5x-150) is x<=-10/3 \lor x>= 15/4