Question

Is it possible for x=-2 to be in the domains of the function:
R(x)= 3x^3-5x+6
--------------
x+2

Answer 1

Only if 3x^3-5x+6 has a factor of x+2

Answer 2

But if x + 2 was a factor, wouldn't that cause a hole, meaning its undefined..

Answer 3

Good point. It's not a factor anyway so... :)

Answer 4

I was thinking in terms of limits.... =/

Answer 5

So the answer is no because why?

Answer 6

Can you have a 0 in the denominator of a fraction?

Answer 7

no

Answer 8

:) That's why...

Answer 9

The question just asks if its possbile

Answer 10

oh Thanks sry i have never used this before.

Answer 11

the second part of that ? is

Answer 12

np... :) I appreciate that you did ask "why" though. Many people who post here don't care to know why....they just want the answer.

Answer 13

second part is what?

Answer 14

H(x)= square root x+1

Answer 15

Yeah I want to learn how to do them not just get the answers.

Answer 16

I have a few more but cant figure ourt how to type them to you. lol

Answer 17

is that sqrt(x + 1) or sqrt(x) + 1? ANd what are you looking for to be in the domain?

Answer 18

it just says x+1 with no ()s

Answer 19

-2

Answer 20

Is the x+1 under the sqaure root sign, or is the 1 on the outside?

Answer 21

OH! Sorry all under the square root sign

Answer 22

we use the parentheses to show that... (for future reference when typing these) :) So you have sqrt(x + 1). Can you take the square root of a negative number?

Answer 23

I didnt think so.

Answer 24

you cant have a neg inside the sqrt

Answer 25

right?

Answer 26

In order for a number to be part of the domain, you have to be able to evaluate the expression at that number. So for x = -2 to be in the domain, you have to be able to evaluate sqrt(-2 + 1) = sqrt (-1).

Answer 27

Right...so since you can't take the sqrt of a negative...is x = -2 in the domain? ;)

Answer 28

no?

Answer 29

lol...try again with confidence!

Answer 30

I have to write out why or why not. So I would just answer this by saying you cant take the sqrt of a neg #?

Answer 31

Haha. No!

Answer 32

That's beter! we'll make a mathematician out of you yet!

Answer 33

What do you do for a living cause you should be a teacher. lol I like the way you teach!

Answer 34

I used to be a teacher...college math. then i decided to join the military for a change. when i get out, i plan to go back to teaching. :)

Answer 35

Ok here is another one.. Suppose we are given two functions f(x)= 3x+2-4/x and g(x)= 2-3x. find the indicated values:

f(a+b)

Answer 36

if i asked you to find f(3), could you?

Answer 37

Well you are VERY good at it and I like that you throw in some positiveness!! ha.

Answer 38

Yes

Answer 39

Then do the same thign...only use a+b instead of 3 :)

Answer 40

I am not very good with fractions :(

Answer 41

ohh. I get it! Der.

Answer 42

embrace the fraction!

Answer 43

I am kinda confused on the last part thou

Answer 44

4/a+b? <-- is that how I would write it?.

Answer 45

is the problem \[3x+2-\frac{4}{x}\]?

Then the answer would be \[3a+3b+2-\frac{4}{a+b}\]

Answer 46

hey how did you do that? lol

Answer 47

lol...the equation editor :)

Answer 48

I cant fail this assignment so thank you so much for helping me!!

Answer 49

\frac{}{} is the code for a fraction. put the numerator in the first set of curlies and the denominator in the second set

Answer 50

wrap it inside of a \[

Answer 51

and a \]

Answer 52

so... slash[\frac{3}{4}\] (replacing the wotrd "slash" with a "\") will give you \[\frac{3}{4}\]

Answer 53

The second part of that ? is: g(a)-g(a-b)+f(a

Answer 54

Go slowly...evaluate each part [g(a), g(a-b) and f(a)]
then connect them together as requested...

Answer 55

Wheter or not you need to combine the fractions is up to your instructor. personally, unless i'm working with common denominators, i wouldn't have my students worry about it.

Answer 56

this one really confuses me

Answer 57

the purpose of the problem is to get you to understand the mechanics of evaluating at non-numbers...not to cause problems with nasty denominators.

Answer 58

what is g(a)? we'll start there

Answer 59

I know i need to plug that in where x is but do i plug that whole thing in

Answer 60

for g(a), you just plug a in for x...

Answer 61

so g(a)=-3(a)

Answer 62

g(x) = 2-3x...

Answer 63

opps . i left out the 2

Answer 64

so in place of the x i put a. g(a)=2-3(a)?

Answer 65

right...so what is g(a-b)?

Answer 66

g(a-b)=2-3(a-b)?

Answer 67

distribute...

Answer 68

ga-gb=2-3a+3b?

Answer 69

well...you don't distribute the g(a-b) part...since g is a function...ut the right side is correct.

Answer 70

finally, what is f(a)?

Answer 71

Ohh. Opps. Im not good at math at all. Splendid in english thou :)

Answer 72

f(a)=2-3a?

Answer 73

we'll get you there. :)

Answer 74

nope...that is the function g...not the function f

Answer 75

remember, the function f is f(x) = 3x+2-(4/x)

Answer 76

Uh. Help?!

Answer 77

lol...g(x) and f(x) are two different functions. just like your cofee maker and dishwasher have two different functions.

Answer 78

lol...g(x) and f(x) are two different functions. just like your cofee maker and dishwasher have two different functions.

Answer 79

lol...g(x) and f(x) are two different functions. just like your cofee maker and dishwasher have two different functions.

Answer 80

lol...g(x) and f(x) are two different functions. just like your cofee maker and dishwasher have two different functions.

Answer 81

haha um

Answer 82

i don't know why that happened.

Answer 83

g(x) = 2-3x and f(x) = 3x+2-(4/x), right?

Answer 84

I didnt know the two functions went together

Answer 85

right

Answer 86

thats tricky.

Answer 87

putting them together is like making coffee then putting the pot in the dishwasher. so what we do is we evauate each piece...then string them together.

Answer 88

Given the functions f(x) = 3x + 2- 4/x
and g(x) = 2 - 3x, fnd the indicated values.
a) f(a + b)
b) g(a) - g(a - b) + f(a)

Answer 89

right...so for part b) so far we have that...

Answer 90

a) is the first one and b) is the second they mushed together

Answer 91

g(a) = 2-3a

Answer 92

g(a-b) = 2-3a+3b

Answer 93

what is f(a)? next we'll mash them together...