Answer:
Option D is the correct option.
<em>please </em><em>see</em><em> the</em><em> attached</em><em> picture</em><em> for</em><em> full</em><em> solution</em><em>.</em><em>.</em>
<em>Hope</em><em> </em><em>it</em><em> </em><em>helps</em><em>.</em><em>.</em><em>.</em>
<em>Good</em><em> </em><em>luck</em><em> on</em><em> your</em><em> assignment</em><em>.</em><em>.</em><em>.</em>
Answer:
The domain is {x : x ∈ R} or (-∞ , ∞)
Step-by-step explanation:
* Lets explain how to find the domain
- The domain of the function is the values of x which make the
function defined
- The quantity under the square root must be ≥ 0 because there is
no square root for negative value
* Lets solve the problem
∵ f(x) = √(x² - x + 6)
∴ The value of (x² - x + 6) must be greater than or equal zero because
there is no square root for negative value
- Graph the function to know which values of x make the quantity
under the root is negative that means the values of x which make
the graph under the x-axis
∵ The graph doesn't intersect the x-axis at any point
∵ All the graph is above the x-axis
∴ There is no value of x make f(x) < 0
∴ x can be any real number
∴ The domain of f(x) is all real numbers
∴ The domain is {x : x ∈ R} or (-∞ , ∞)
