What is the domain of the function √( 2x^2+7x+3)?

Question

how do you find the domain of the function?

Answer 1

We know that g(x) = √[f(x)] iff f(x) > 0. So this function is defined only when:



2x^2 + 7x + 3 > 0

==> (x + 3)(2x + 1) > 0



We know that parabolas that have a positive leading coefficient are negative only on the interval with it's roots as the end-points and positive elsewhere. Since the zeroes of this are x = -3 and x = -1/2, we can conclude that this function is defined on:



(-infinity, -3] U [-1/2, infinity).



I hope this helps!

Answer 2

The domain are all the points you can put "inside" the function. It is the values you can evaluate your function in.



The square root function has only 1 problem with its domain: The negative values.



Assuming this is a question in the Real domain and not complex numbers, square roots of negative numbers just can't be, so, as long as 2x^2+7x+3 is positive or zero, theres no problem! AKA the domain.



therefore, solve



2x^2+7x+3 >= 0



You will probably get 2 points, which are the points where the parabola crosses the x axis. The points in the middle are negative, so those points are the problem.



Lets do it:



2x^2+7x+3 > 0 /apply formula (discriminant is positive, so there is no problem)



x1 = -0.5

x2 = -3



Then the picture would be a Parabola that intersects the X axis in those 2 points. That means that the points between x1 and x2 are all negative while all the other points are positive (or zero)



Then the domain is ]-infinity to -3], [-0.5 to +infinity[

Answer 3

All x such that 2x² + 7x + 3 ≥ 0



(2x + 1)(x + 3) ≥ 0



Two cases:

Case 1:

2x + 1 ≥ 0

and

x + 3 ≥ 0



2x ≥ -1

x ≥ -1/2

x ≥ -3

Condition is met for all x ≥ -1/2



Case 2:

0 ≥ 2x+1

and

0 ≥ x + 3



-1 ≥ 2x

-1/2 ≥ x

-3 ≥ x

Condition is met for all x ≤ -3



Therefore the domain of the function is x in (-∞, -3] U [-1/2, ∞)

or, in other words the domain of the function is all x except -3 < x < -1/2



The first response is correct except that -3 and -1/2 are not excluded but are part of the domain.

Answer 4

Domain includes all the values of x where the expression returns a real answer

This means no dividing by zero, and, in this case, no squareroots of negatives



So you find at what point 2x^2+7x+3>=0

This factors to (2x+1)(x+3)>=0

x=0 at -1/2 and -3



If x is greater than -1/2, both factors become positive, making the end result positive

If x is less than -3. both factors become negative, making the end result positive

If x is between the two, only one factor is negative, making the end result negative, and generating an imaginary number when it's squarerooted



Your domain is [-∞,-3] and [-1/2,∞]

Answer 5

The "area: of a function is all the x values that are blanketed interior the completed function. be sure the area by potential of asking "What can x not equivalent?" The "variety" of a function is all the y values that are blanketed interior the completed function. be sure the style by potential of asking "What can y not equivalent? (4) is calling you "Can M be the x and R be the y OR can M be the y and R be the x? Why or why not?"