finding domain and range of functions [PLEASE HELP !]?

Question

find the domain and range of each function; ex: (-3, inf.]

1. f(x)= squareroot of x^2+4
2. h(x)= 5/x-3
3. f(x)= 3x-1/(x+3)(x-1)
4.f(x)= 1/x + 5/x-3
5. g(x)= x/x^2-5x
6. h(x)= squareroot 4-x^2 / x-3
[THE DENOMINATOR IS NOT UNDER THE RADICAL; only 4-x^2]

7.h(x)= squareroot 4-x/ (x+1)(x^2+1)
[THE DENOMINATOR IS NOT UNDER THE RADICAL; only the 4-x]

8.f(x)= squareroot x^4-16x^2

FIND THE RANGE ONLY [9-12]
9. f(x) 10-x^2
10. g(x)= 5+ squareroot 4-x
11.f(x)= x^2/1-x^2
12. g(x)= 3+x^2/4-x^2


THAT'S ALL; I'LL CHECK BACK ON THIS Q EVERY FEW MINUTES. ASK FOR ANY CLARIFICATIONS IF YOU NEED THEM.

I WOULD DO IT IF I KNEW HOW. that's why i asked this question! cause i don't. duh, common sense

Answer 1

Break it up into several questions, to motivate people to answer and get more points..
I'll demonstrate a couple, and you can apply them to the others

1.
f(x)= sqrt (x^2+4)

Domain:
Check and see what values are limited by the function, and you know the domain. Since there is a square root in this function, you know that whatever you are taking the square root of cannot be < 0. Can "x^2 + 4" be < 0? No, because you square "x", and that expression will always be positive. So your domain is:
(-infinity, infinity)

Range:
Solve for "x":
y = sqrt(x^2 + 4)
y^2 = x^2 + 4
x^2 = y^2 - 4
x = sqrt(y^2 - 4)
Again, see where "y^2 - 4" is less than 0
y^2 - 4 < 0
y > -2 or y < 2 limits the range
So, y must be greater than 2 or less than -2
Range: (-infinity,-2]U[2,infinity)

2.
h(x) = 5 / (x-3)

Domain:
denominators cannot equal zero, so "x - 3 = 0" limits the domain
x - 3 = 0
x = 3 limits the domain
Domain: (-infinity,3)U(3,infinity)

Range:
y = 5/(x - 3)
y*(x - 3) = 5
yx - 3y = 5
yx = 5 + 3y
x = (5 + 3y) / y
y cannot equal zero, so
Range: (-infinity,0)U(0,infinity)

3.
f(x)= 3x-1/(x+3)(x-1)

Domain:
Again, the denomintors limit the domain
(x + 3) cannot equal zero
(x - 1) cannot equal zerp
x = -3 and x = 1 limite the domain
Domain: (-infinity,-3)U(-3,1)U(1,infinity)

Range:
y = 3x-1/(x+3)(x-1)
Nothing limits the range here; y can equal zero, because there is an "x" term in the numerator.

Answer 2

For the domain: If the function involves fractions, then set the denominator equal to zero and solve for the variable.
Example: #2
h(x) = 5/(x-3)
x-3 = 0
x = 3
Domain = all real numbers except 3.
If the function involves a square root, then set whatever is underneath the square root greater than or equal to zero and solve for the variable. This will be your domain.
Example: #8
f(x) = sqrt(x^4 - 16x^2)
x^4 - 16x^2 >= 0
x^2(x^2 - 16) >= 0
x^2(x-4)(x+4) >= 0
Your critical points occur when
x^2 = 0, x-4 = 0 or x+4 = 0
x = 0, x = 4 or x = -4
x^4 - 16x^2 is greater than or equal to zero when
x <= -4, x = 0, x>= 4
Domain = (-infinity,-4] U {0} U [4,infinity)

Answer 3

a internet site is the set of x values that are usable contained in the equation the variety is the set of y values that be conscious to the equation. for the 1st question, the variety is YER y is an ingredient of all genuine numbers consequently there are no regulations. the area is likewise XER, x is an ingredient of all genuine numbers as no x fee will create a undefinable fee of y. for the 2d functionality, you will desire to evaluate truthfully the fee indicators | . . . | they advise that the fee contained in the field will develop into helpful. consequently the area continues to be XER, yet now y would desire to be equivalent to or greater advantageous than 0 as that's going to be helpful. variety = y>= 0 the third question is a similar ingredient. because of the fact the fee of x is being squared, the respond will consistently be helpful (that's additionally because of the fact the subsequent fee is being extra no longer subtracted). any even exponent will provide an excellent sort whilst an odd (3, 5, 7) will provide a unfavourable fee whilst x is unfavourable. you will desire to evaluate that when the x fee is calculated with the exponent, a million is extra to it. so the area continues to be XER however the variety is now y is comparable to or greater advantageous than a million simply by +a million. a accepted rule is that until eventually there's a denominator with x in it, ie (some fee/(x or an equation with x in it), then the area is XER. the variety is what maximum generally variations solid success wish it helps!

Answer 4

That's all? Are you serious? You need to stay after school for tutoring with your teacher.

Or, is this another example of a math teacher that gives worksheets for homework? You know, those where the teacher only grades the answers.

The answers in mathematics are secondary to the processes used to arrive at those answers. Get to reading your book and thinking on your own. Pick one questions and then ask.

See the following for insight into your simpler problems:
http://answers.yahoo.com/question/index;_ylt=AooOKXE3L_F54.kfEuDjO6fsy6IX?qid=20060809102632AAweN6H

Answer 5

if you don't do your own work, or at least , double check the "answers" you are given.

How will you learn ? How poorly will you do on a test or quiz where you don't have internet availabilty?

How would you know if the answers where even close to being correct..some responders could give you the wrong answers


Math is not all that hard....if YOU work at it

Answer 6

There are lots of people who would make fun of the prospect of altering their destinies. This is due to the fact that it believes that no one gets more that what is put in his fate.