Find the domain for the function f(x)=sqrt x^2-x+6
1 answer:
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 (-∞ , ∞)
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Answer:
Second point (-5/2, -7/2)
First point (3/2, 17/2)
Step-by-step explanation:
We have two equations, and we want to know at wich poin are equal. Hence, we have a system of equations and the solution is nothing more that the point (x,y) where those functions intercepts.
4x2+ 7x -11=y
3x+4=y
Lets use substitute method
4x2+7x-11=3x+4
This can be re arrange as the following eq:
4x2+4x-15=0
A quadratic equation, its solution can be obtained using the below eq.
where a=4, b=4, c=-15.
Remember, the quadratic equation as a +/- sign, meaning that you will obtain one answer using the + operator and other using the - operator.
By doing the above, we have x=-5/2 and x=3/2
By using x=3/2 in equation of line (3x+4=y) we have y=17/2
First point (3/2, 17/2)
By using x=-5/2 in equation of line (3x+4=y) we have y= -7/2
Second point (-5/2, -7/2)
Those points are the ones where the line and the parabola intercept.