Question

How do you find the domain and range for f(x)= x^2+x-2/x^2-3x-4 when factored it looks like this (x+2)(x-1)/(x+1)(x-4)

Answer 1

I responded to your other question bro

Answer 2

i know this is my last one i have a problem with.. im srry im just confused

Answer 3

There are a couple of things to know which is

1. For the domain: The denominator cannot equal zero, therefore (x+1)(x-4) = 0 is invalid. In other words, the x values that make that expression true are invalid.

2. For the range: You need to find a value (if any) that would cause you not to be able to find an x value. If you try f(x) = 0, you'll just end up with 0 = (x+2)(x - 1) but that expression is in the numerator so those x values are valid. Now you'll have to think of another value for f(x) that would cause your function to be invalid. Can you think of anything? I can't.

Answer 4

No i can't.. did i write it wrong? or is there no domain or range

Answer 5

There is a domain and range. What I've done is help you figure out what values we can possibly eliminate from the domain or range.

Basically, what you do with domain and range is assume that the domain is all real numbers and assume that the range is all real numbers unless you can find values that can be eliminated from the domain or range. Then the domain or range will be all real numbers EXCLUDING the values that are invalid.

Answer 6

So the domain is -2 and 1?

Answer 7

If you assume that the domain is all real numbers, you want to find the values that are not included in the domain. -2 and 1 are in the domain so you don't worry about them.

Answer 8

Don't worry about them for the range right because i have -2,1,1,4

Answer 9

im sorry -2,1,-1,4

Answer 10

@kozy, hire a personal tutor for these because you need someone with a whiteboard who can explain it to you.

Answer 11

okay thanks for your help

Answer 12

Have you found the domain ?

Answer 13

i think its -2 and 1 but idk if im right

Answer 14

Write the denominator here?

Answer 15

(x+1)(x-4)

Answer 16

Equate it to 0, what would you get for x?

Answer 17

you'll get -1 and 4

Answer 18

These values of x, will make denominator 0 and f(x) will be undefined for these values. So
domain is all real numbers except -1 and 4
\[R-\text{{-1, -4}}\]

Answer 19

How about range that's the hard one for me

Answer 20

Sorry, I made a mistake
It'd be
\[R-\text{{-1, 4}}\]

Answer 21

Let's find the range :)

Answer 22

\[F(x)=\frac{(x+2)(x-1)}{(x+1)(x-4)}\]
Let f(x) be y
\[y=\frac{(x+2)(x-1)}{(x+1)(x-4)}\]
Can you find x in terms of y.??

Answer 23

@kozy ???

Answer 24

Proper Notation
\[\left \{x \in R : x \ne-1, x \ne 4 \right \}\]

Answer 25

I'm sorry what do you mean by finding x in terms of y?

Answer 26

Suppose I have
\[y=2x\]
so x in terms of y is
\[x=\frac{y}{2}\]
You have to cross multiply and solve for x

Answer 27

oh okay let me try

Answer 28

take your time :)

Answer 29

I'm sorry i'm stuck i don't know how to do that with the function we're using

Answer 30

Oops I just realized that's it's difficult here, put x= infinity, what'd you get for y?

Answer 31

infinity, 1 union infinity -4 ?

Answer 32

I mean what you'd get for f(x), if you put x=\(\infty\) in f(x)

Answer 33

i'm stuck :(

Answer 34

ok, tell me what's
\[\frac 1 \infty\]

Answer 35

0

Answer 36

good, divide numerator and denominator by x
\[y=\frac{(x+2)(x-1)}{(x+1)(x-4)}\]

Answer 37

then put x=infinity

Answer 38

\[\large y=\frac{(1+\frac 2 x )(1-\frac 1x )}{(1+\frac 1 x)(1-\frac 4x)}\]
now put x= \(\infty\)

Answer 39

okay i got it! now which side is the range?

Answer 40

what did you get for y?

Answer 41

Hey @ash2326, help him with his previous problem.

Answer 42

(1+2/infinity)(1-1/infinity) ? im a girl :)

Answer 43

By the way, finding the range is much simpler than you think.

Answer 44

\[\large y=\frac{(1+\frac 2 x )(1-\frac 1x )}{(1+\frac 1 x)(1-\frac 4x)}\]
put x=\(\infty\)
\[y=\frac{(1+0)(1-0)}{(1+0)(1-0)}=????\]

Answer 45

oh right!! im sorry

Answer 46

so y = 1?

Answer 47

yes, this is the value of y when x is infinity.
so range is all real no.s except 1

Answer 48

Are you sure about that @ash2326?

Answer 49

thank you

Answer 50

I'm 100% sure the range is all real numbers

Answer 51

are you sure @hero

Answer 52

Yes. The reason why is because if you substitute f(x) with any number, you will be able to solve for x. If you are able to solve for x after substituting f(x) with a number, then that number is in the range.

Answer 53

So if we take f(x) = 1 and we are able to solve for x, then 1 is in the range of the function. We need to find values that are out of the range. But we won't find any such number.