Question

What is the domain of the function f(x)=x+1/2x-1?
I absolutely cannot do domain and range for some reason. Please help me!!

Answer 1

Do you know that you cannot divide by 0?

Answer 2

yes.

Answer 3

Do you know, therefore, that the denominator of a fraction cannot be 0?

Answer 4

yes

Answer 5

What is the denominator of your fraction?

Answer 6

2x-1

Answer 7

So, it would be illegal for 2x-1 to be 0. Do you agree?

Answer 8

Yes I agree...

Answer 9

What value of x would therefore be illegal?

Answer 10

if 2x-1=0 then 2(.5) would equal 1 and 1-1 would equal 0. So x cannot equal .5 right?

Answer 11

That is correct. So just remember that for a minute.

Answer 12

Do you know the definition of domain?

Answer 13

umm... all I know is my teacher usually has us put it in set builder notation. So I would have to say something along the lines of {x|x does not equal 0}

Answer 14

The domain is the gazillions of values that x CAN be. We know that x CAN'T be 1/2 but it CAN be everything else. And that everything else is the domain.

Answer 15

So if we start with negative infinity on a number line and go to the right until we get to 1/2...all of those numbers are in the domain. Then we skip 1/2 and go on to the right to positive infinity and all of those numbers are in the domain.

Answer 16

\[{x|x \in \mathbb{R} \neq .5}\]

Answer 17

is that what you're saying?

Answer 18

There are basically three ways to show those numbers:
1. On a number line
2. Interval notation
3. Set builder notation

Answer 19

And yes, what you wrote is correct is you put the braces around it that make it a set.

Answer 20

*if

Answer 21

Do you understand?

Answer 22

That makes so much more sense... can you be my math teacher from now on? :D

Answer 23

Sure

Answer 24

Lol that's amazing! Thanks so much! While you're here... could you help me with another question?

Answer 25

yes

Answer 26

Ok so the one I have a question on is: What are the roots of the equation x^2+5x-3=0?

Answer 27

Well, that won't factor so we have two choices for solving it:
1. Complete the square
2. Use the quadratic formula.

Answer 28

Which method do you prefer?

Answer 29

Can we try option 1: complete the square?

Answer 30

Sure.

Answer 31

Here are the steps:
1. Move the 3 to the right side.

Answer 32

2. Divide the coefficient of x by 2

Answer 33

3. Square that number

Answer 34

4. Add that number to both sides.

Answer 35

5. Factor the left side

Answer 36

6. Take the square root of both sides

Answer 37

Do you mean divide x^2+5x by 2?

Answer 38

No. The coefficient of x is 5. Divide 5 by 2

Answer 39

And just leave it in the form 5/2

Answer 40

gotcha

Answer 41

but wouldn't we have to factor the entire side to make it equal and what not? (sorry I'm just making sure I understand you.)

Answer 42

Yes. After you make it factorable.

Answer 43

\[x^2+5x=3\]
\[x^2+5x+(\frac{5}{2})^2=3+(\frac{5}{2})^2\]

Answer 44

Now it is factorable

Answer 45

I see! Thanks! :D

Answer 46

\[(x+\frac{5}{2})^2=\frac{12}{4}+\frac{25}{4}\]

Answer 47

\[(x+\frac{5}{2})^2=\frac{37}{4}\]

Answer 48

Now take the square root of both sides.

Answer 49

\[\sqrt{(x+\frac{5}{2})^2}=\pm \sqrt{\frac{37}{4}}\]

Answer 50

\[x+\frac{5}{2}=\pm \frac{\sqrt{37}}{2}\]

Answer 51

\[x=- \frac{5}{2}\pm \frac{\sqrt{37}}{2}\]

Answer 52

I get it!!! Awesome! Thank you so much!

Answer 53

yw