What is the domain of f(x)=sqrt(2x^2-7x-15) ?

The domain of f(x)=sqrt(2x^2-7x-15) is x = 5

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domain of f(x)=sqrt(2x^2-7x-15)

domain

f (x) = 2 x^{2} - 7 x - 15

x \leq - \frac{3}{2} or x \geq 5

Interval Notation

(- \infty, - \frac{3}{2}] \cup [5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{3}{2} or x \geq 5

The function domain

x \leq - \frac{3}{2} or x \geq 5

What is the domain of f(x)=sqrt(2x^2-7x-15) ?
The domain of f(x)=sqrt(2x^2-7x-15) is x<=-3/2 \lor x>= 5