Answer:
(x ≤ -4) ∪ (x ≥ 1.5)
Explanation:
You want the domain of f(x) = √(x² +5x -12).
Square root
The domain of the square root function is the set of values of the variable where the radicand is non-negative.
Quadratic
The quadratic can be factored as ...
2x² +5x -12 = (x +4)(2x -3)
Zeros of this product are x = -4 and x = 3/2. The product will be negative for x-values between these zeros: -4 < x < 3/2.
Domain
The domain of f(x) will be those values of x that do not make the quadratic negative:
(x ≤ -4) ∪ (x ≥ 3/2)
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