What is the domain of the radical function f of x is equal to the square root of the quantity 2 times x squared plus 5 times x minus 12 end quantity.

Question

asked Sep 6, 2024 101k views

1 Answer

Rashaun · Answer 1 · 2024-09-11T02:51:45+0000

Answer:

(x ≤ -4) ∪ (x ≥ 1.5)

Explanation:

You want the domain of f(x) = √(x² +5x -12).

The domain of the square root function is the set of values of the variable where the radicand is non-negative.

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.

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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