5

1] Find the domain of the following functions_f(x) =V-x2+3x + 10 [15 pts] 4 b) f(x) =Er"-I-1 [15 pts] f(r)-75 ~u-Tr [15 pts]...

Question

1] Find the domain of the following functions_f(x) =V-x2+3x + 10 [15 pts] 4 b) f(x) =Er"-I-1 [15 pts] f(r)-75 ~u-Tr [15 pts]

1] Find the domain of the following functions_ f(x) =V-x2+3x + 10 [15 pts] 4 b) f(x) =Er"-I-1 [15 pts] f(r)-75 ~u-Tr [15 pts]



Answers

Find the domain of the function f given by each of the following. $$ f(x)=\frac{1+x}{3 x-15 x^{2}} $$

We need to find the domain in here. There are no restrictions. No matter what X value we plug in, we're going to get a Y value. So our domain consists of all numbers, from negative infinity to positive infinity.

Or go for this problem is to find the domain of each function. So first we have one over one plus you. To the acts Well notice that the domain here can only be restricted by the denominator. If this was undefined and the only way this could be undefined, this fraction would be if the denominator equal zero, Meaning each of the X has to equal and negative one. In order for this to equal zero. And we know this, there's no way this can equal zero. So therefore the domain is all real numbers. There's never a point where it's on the fine. Now, if we look at 1/1 minus E to the X story because we see that um if X equals zero, then we have one minus one. So now the denominator is undefined or the denominator zero. And the functions undefined. So where do we go from negative infinity to zero And then from 0 to Infinity, but not including zero.

Let's say we had the equation y two equals X minus for over. Expert was two x minus 15. Since we're dividing by a variable, you know we can't divide by zero, so you do not want X squared plus two x minus 15 to be equal to zero. You don't want that. This is fact herbal. It's a quadratic well, multiplies the negative 15 and asked a positive to positive five in negative three so we wouldn't want the Factor X Plus five to be equal to zero. Nor would we want the factor x my mystery to be equal to zero. So if he's attracted five and add three, that's telling us, Try it again, that we wouldn't want extra Pete. You're negative five or positive three. Because if it was, we wouldn't be divided by zero. You can't do that. So the domain, everything else is going to be fair game. We can put anything from negative infinity up to negative five not included from negative 5003 included. Not included. Excuse me and from three deposited Anthony included. Those are all be eligible inputs into the domain of this function

In this problem, I want to find the domain for the function F. Of X equals the quantity five X plus three. Over the quantity four X minus one. So the first part here is my numerator, the five X plus three. And that has a domain of all real numbers. And then the second part is the denominator, the four X -1. And there is a restriction on this. We cannot have a denominator that's equal to zero. So I need to figure out what value of X would make it equal to zero. So I'm gonna solve this out. So X Is going to equal 1/4. So any number, Any real number can be used in this spot for ex except for 1/4 because 1/4 makes it zero and that's not allowed. So we can have X can be less than 1/4. X can be greater than 1/4 but X cannot equal 1/4. So an interval notation, the domain looks like negative infinity to 1/4, parentheses. E and parentheses E. 1/4 to infinity. And these are parentheses because the 1/4 is not included in the domain.


Similar Solved Questions

5 answers
QUESTIONcompany Intorestod knowing It tharo saquonce und tho numbor relatlonatip batwean Otton Ia nuber that ar made ot houn that Comnula Omo O [Yaluo baincd lora coelcated tha quostions bolow; doscribo the relationshp betwocnhou MaLoua pta each) 0t babing ud euorrutoa TelELLHour ot Training Q) :Fmon; Tino ZXYcomputation , uaunl:Iao
QUESTION company Intorestod knowing It tharo saquonce und tho numbor relatlonatip batwean Otton Ia nuber that ar made ot houn that Comnula Omo O [Yaluo baincd lora coelcated tha quostions bolow; doscribo the relationshp betwocnhou MaLoua pta each) 0t babing ud euorrutoa TelELL Hour ot Training Q) ...
5 answers
(10 points)Section 4.5Evaluate the following integrals: (tan d~, where C : I:l =1/2(cos ~ + e? dz, where C : |z - 1/ = 1/2 2 _ [)"(8 points) Section 4.6 Evaluate the following integral by using Causs' Mean Value Theoremsec(eie de
(10 points) Section 4.5 Evaluate the following integrals: (tan d~, where C : I:l =1/2 (cos ~ + e? dz, where C : |z - 1/ = 1/2 2 _ [)" (8 points) Section 4.6 Evaluate the following integral by using Causs' Mean Value Theorem sec(eie de...
5 answers
LO1-2Need Help? Read ItTelk to & TutorWatch It41 points SCalc8 1.3.502 XP'0lFind f 0 9 0 h. f(x) =X+ 5 g(x) = 3x, h(x) =x- 1Need Help?Road Itwatch ItTolkto TutorSubmit AnswerSave ProgressPractice Another VersionType here to searchQ
LO 1-2 Need Help? Read It Telk to & Tutor Watch It 41 points SCalc8 1.3.502 XP '0l Find f 0 9 0 h. f(x) =X+ 5 g(x) = 3x, h(x) =x- 1 Need Help? Road It watch It Tolkto Tutor Submit Answer Save Progress Practice Another Version Type here to search Q...
5 answers
Consider the following differentlal equation to be solved by varlatlon of parameters 4y" Y = e*/2Find the complementary function of the differential equation_
Consider the following differentlal equation to be solved by varlatlon of parameters 4y" Y = e*/2 Find the complementary function of the differential equation_...
5 answers
EElnEttonDitt.Arln4 `Re €CEDIESniinLeonk DaCoenn HD -Etmhenr ~LeenranaelEmeaLatRLoeeannLaeLedTaeN [erliaEele En Ea eeAEln Eet TEenEdee neenenneineetEetanteene mtenn74dcArlleAottadodiortred DAerentunne LLleceet He Fen ReIC LAabezl Mttt HI TteEe ae UeanEen Ledeln )Red Ereel #EledieCEFtanr
EElnEtton Ditt. Arln4 ` Re €CEDIESniinLeonk DaCoenn HD -Etmhenr ~LeenranaelEmeaLatRLoeeannLaeLed TaeN [erlia Eele En Ea ee AEln Eet TEenEdee neenenneineetEetanteene mt enn 74dcArlleAottadodiortred DAerentunne LLleceet He Fen ReIC LAabezl Mttt HI TteEe ae Uean Een Ledeln ) Red Ereel #Eledie CE...
5 answers
Rewrite &he iunctiom t0 fimd $' (x) fr f(s} =- 1f() = Imq2r' +1)
Rewrite &he iunctiom t0 fimd $' (x) fr f(s} =- 1 f() = Imq2r' +1)...
1 answers
A 500 -g collar can slide without friction along the semicircular rod $B C D .$ The spring is of constant $320 \mathrm{N} / \mathrm{m}$ and its undeformed length is $200 \mathrm{mm} .$ Knowing that the collar is released from rest at $B$, determine (a) the speed of the collar as it passes through $C,(b)$ the force exerted by the rod on the collar at $C$
A 500 -g collar can slide without friction along the semicircular rod $B C D .$ The spring is of constant $320 \mathrm{N} / \mathrm{m}$ and its undeformed length is $200 \mathrm{mm} .$ Knowing that the collar is released from rest at $B$, determine (a) the speed of the collar as it passes through $C...
5 answers
(3) Complete the following table Molecule #of Lewis dot valence @ structureMolecular dipole? (Yes or No)Molecular geometrySiH4CO3?CH:SHIdentily the geometry for and S as central aloms Electronegativily values: H-2.1; C-2.5; 8-2.5; 0-3.5, F-4.0; Si=1.8; N-3.0; Cl-3.0.
(3) Complete the following table Molecule #of Lewis dot valence @ structure Molecular dipole? (Yes or No) Molecular geometry SiH4 CO3? CH:SH Identily the geometry for and S as central aloms Electronegativily values: H-2.1; C-2.5; 8-2.5; 0-3.5, F-4.0; Si=1.8; N-3.0; Cl-3.0....
5 answers
Which of the spectral series follows the spectral line emittedfrom the mercury atom when applying voltage 4.9 V?
Which of the spectral series follows the spectral line emitted from the mercury atom when applying voltage 4.9 V?...
5 answers
Fill in the table / below for the Initial concentratons 5 Solution 'reactant and the rate [HzOzk reaction. [KIJa #.4 Rate kPa/s mollz Rate Mi 1OO m"/i 0.0403 I-lo" 58 *i0-5Determine the rate law for the decomposition of H,Oz in the presence0For each reaction, calculate the rate constant; k
Fill in the table / below for the Initial concentratons 5 Solution 'reactant and the rate [HzOzk reaction. [KIJa #.4 Rate kPa/s mollz Rate Mi 1OO m"/i 0.0403 I-lo" 58 *i0-5 Determine the rate law for the decomposition of H,Oz in the presence 0 For each reaction, calculate the rate con...
3 answers
Solve Axy dx + (2x2 -[) dy = 0
Solve Axy dx + (2x2 -[) dy = 0...
5 answers
In the figure; four long straight wires are perpendicular to the page; and their cross sections form square of edge length a 10.5 cm. Each wire carries 8.00 A,and the currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3.In unit-vector notation; what is the net magnetic force per meter of wire length on wire 4?Number2.08E-42.08E-4jUnits
In the figure; four long straight wires are perpendicular to the page; and their cross sections form square of edge length a 10.5 cm. Each wire carries 8.00 A,and the currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3.In unit-vector notation; what is the net magnetic fo...

-- 0.018678--