Question

Let f(x) = 2-x and g(x) = 1/x. Perform each function operation and then find the domain of the result. g/f(x)

Answer 1

I thought I helped you with this already.

Answer 2

would it be 1/2x-x^2

Answer 3

equate denominator=0 and omit that x values for domain

Answer 4

Yes, and by the way: (General Rule)

\[\frac{a}{b} \div \frac{b}{a} = \frac{a}{b} \times \frac{a}{b}\]. In other words, flip the second fraction

Answer 5

Yes, and make sure that the denominator doesn't equal zero

Answer 6

\[2x - x^2 \ne 0\]

Answer 7

domain={R/x not equal to 0 and 2}

Answer 8

(-\[(-\infty,0]U[0,2]U[2,\infty)\]

Answer 9

thangiee's answer completly confused me.

Answer 10

\[(1)/(2x-x^2)\]

Answer 11

\[x(2-x) \ne 0\]\[x \ne 0 \space \text{and} \space x \ne -2\]

Answer 12

^ That refers to the domain @trolololcat

Answer 13

Remember, we're saying that the not equal sign means that x cannot equal zero and x cannot equal negative 2 because that would make the denominator equal zero, which is a "no-no" in math because we cannot divide by zero....ever! :D

Answer 14

1/0 is undefined

Answer 15

So basically, what we mean is that when you post your solution to (g/f)(x), include what the domain cannot equal as part of your answer.

Answer 16

To find the domain you always set the denominator to =0 and solve?

Answer 17

Yes

Answer 18

yes but
should omit that x values

Answer 19

And that would help you find out what x cannot equal. I prefer to write it with the not equal sign

Answer 20

Which I demonstrated earlier

Answer 21

ok so when you're dividing you multiply and when you multiple you divide? for this case

Answer 22

Actually, to re-correct myself:

\[x \ne 0 \space \text{and} \space x \ne 2\]

Answer 23

Don't confuse yourself. I told you to go and review what happens when you have a case like

\[\frac{1}{2} \div 3\]

For some reason, you think you're doing something different than basic math when you learned how to multiply by the reciprocal when dividing fractions.

Answer 24

wait, & for \[(x-1)^2/x \] x=1? or it's just left like that fration

Answer 25

I'll look over it. I never really liked fractions, i always tried turning anything into decimals lol

Answer 26

The only thing you have to worry about with regard to the domain and fractions is to make sure that x or any expression in the denominator cannot equal zero.

Answer 27

Can you help me with one more? @Hero
f(x)=2x^2+x-3 g(x)=x-1 (f*g)(x)
So it would be set up like (2x^2+x-3)(x-1) correct?

Answer 28

@Hero

Answer 29

Yes, correct. And the domain is all real numbers because no fraction or square root

Answer 30

Don't forget to multiply and simplify

Answer 31

2x^3+x^2+2x-3

Answer 32

2x^3-x^2+2x-3 I mean

Answer 33

That's probably right. Anyway, I have to go. I want to get a few more episodes of 24 in before I hit the hay.