Question

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

D: [–4, 1.5]

D: [ –4, ∞)

D: (–∞, –4] ∪ [1.5, ∞)

D: (–∞, ∞)

the answer is D: (–∞, –4] ∪ [1.5, ∞)

Answer 1

The domain of a function are the possible input values, the function can take.

The domain of $f(x) = \sqrt{2x^2 + 5x - 12}$ is: $(-\infty, -4]\ u\ [1.5,\infty)$

We have:

$f(x) = \sqrt{2x^2 + 5x - 12}$

Since f(x) is radical, we simply equate the radicand to 0

So, we have:

$2x^2 + 5x - 12 = 0$

Expand

$2x^2 + 8x - 3x - 12 = 0$

Factorize

$2x(x + 4) -3(x + 4) = 0$

Factor out x + 4

$(2x - 3)(x + 4) = 0$

Solve for x

$2x - 3 = 0$ or $x + 4 = 0$

$2x = 3$ or $x = -4$

$x = \frac 32$ or $x = -4$

$x = 1.5$ or $x = -4$

-4 is less than 1.5

So, the domain is:

$x \le -4$ or $x \ge 1.5$

Represent as an interval notation

$(-\infty, -4]\ u\ [1.5,\infty)$

Read more about domain at:

https://brainly.com/question/15339465

Answer 2

Answer:

its c

Step-by-step explanation: