Question

Help with the finding the inverse of a function

Answer 1

@mathmale

Answer 2

Okay so to find an inverse, you want to swap x and y. Lets take:
\[f(x) = 2x-8\]

This is also \[y = 2x-8\]

Now swap x and y to get \[x = 2y-8\] and isolate y

Answer 3

Hello, Decarr!

let's work on finding the inverse of f(x) = 1 / (x+2).

Replace "f(x)" with " y "

Answer 4

y=1/(x+2)

Answer 5

then switch the y and x?

Answer 6

Yes, that's right.

Do that, please, and then please solve the resulting equation for " y "

Answer 7

so x=1/(y+2)?

Answer 8

Yes. now, solve for y+2. Next, solve for y alone.

Answer 9

-2 from both sides?

Answer 10

Can't do that here, because (y+2) is in the denominator.

Answer 11

so just from y then?

Answer 12

\[x=\frac{ 1 }{ y+2 }\]

Answer 13

Solve for (y+2) first. Put (y+2) where x is now, and put x where (y+2) is now.

Answer 14

y+2=1/x?

Answer 15

Yes, very good. Now, subtract 2 from both sides of your equation. what do you get?

Answer 16

y=1/x-2?

Answer 17

that's just a bit ambiguous. Decarr. Please enclose your 1/x with parentheses.

Answer 18

otherwise it might appear that you meant y=1 / (x-2).

Answer 19

or use the fraction
\[y= {1 \over x} -2\]

Answer 20

Roadjester's suggestion is just great. Using parentheses would be a bit faster.

Answer 21

Now, Decarr: replace that ' y '
with the symbol for inverse function of f(x):\[f ^{-1}(x)=\frac{ 1 }{ x }-2\]

Answer 22

... and you're done. Does this result match one of the answer choices?

Answer 23

no it doesn't

Answer 24

Hint: take a careful look at the last (the bottom) answer choice. you are given one fraction.

Separate that fraction into 2 fractions.

Answer 25

Again, compare your result with our tentative answer.

Answer 26

Or multiply 2 by "1" so to speak.

Answer 27

Okay so the answer is (1-2x)/(x) right?

Answer 28

:)

Answer 29

that's the last answer choice given you. That's what I wanted you to look at. But now please separate this one fraction into two parts. One of those parts will be a fraction; the other will be an integer.

Answer 30

I don't understand what you mean sorry

Answer 31

This last answer choice is \[f ^{-1}(x)=\frac{ 1-2x }{ x }\]

Answer 32

This is separable into 2 parts: \[f ^{-1}(x)=\frac{ 1 }{ x }-\frac{ 2x }{ x }\]

Answer 33

Can you reduce the 2nd fraction?

Answer 34

divide by x right?

Answer 35

Yes.

Answer 36

so (1/x)-(2/x)?

Answer 37

I think a more accurate phrasing would be "cancel out" the x's. As opposed to divide by x.

Answer 38

roadjester?

Answer 39

Lead Decarr thru an efficient simplification of \[f ^{-1}(x)=\frac{ 1-2x }{ x }\]

Answer 40

... please ...

Answer 41

Sure.

Okay so, when you have multiple terms in the numerator (top part of a fraction) do you agree you can break it up into multiple parts, all with a common denominator?

Answer 42

thanks, roadjester. I'll be away from my computer for 5-10 minutes.

Decarr: I'd be happy to continue with you later.

Answer 43

Okay thanks for the help now btw have a nice break

Answer 44

That would give you, as mathmale showed above:

\[f^{-1}(x) = \frac {1-2x}{x}={1 \over x}-{2x \over x}\]

Answer 45

okay

Answer 46

If I have say \[\frac {2*2*3}{2*3}\], how would you reduce that?

Answer 47

by getting rid of a 2 and a 3

Answer 48

Okay, good, and what would the final answer be?

Answer 49

no clue math is numbers and gibberish to me sorry

Answer 50

Do you agree the final answer would be just 2? Because if you cancel out in the numerator, it has to be canceled in the denominator as well

Answer 51

yeah

Answer 52

Great, so now let's apply that same concept to

\[f^{-1}(x) = {1 \over x}-{2x \over x}\]

specifically the \[{2x \over x}\] part

Answer 53

Just think of it as \[2*3 \over 3\]

Answer 54

it would be just 2

Answer 55

;)

Answer 56

Exactly!

Answer 57

Thank you, roadjester!

Decarr: Which is the answer to your first problem, A, B, C or D?

Answer 58

Another way to look at is
\[important*junk \over junk \]

Answer 59

Wow! ;)

Answer 60

I think b

Answer 61

or d

Answer 62

Decarr: Look at your most recent result, the one roadjester helped you find.

Which is closest to your recent result, B or D? Why?

Answer 63

I want to say b because it x+8/2 and the 2 is by itself

Answer 64

roadjester has just shown you how you culd break up that ONE fraction into 2 separate parts, and he was right.

But, Decarr, where did that 8 come from? We haven't seen or used 8 anywhere this afternoon.

Answer 65

Okay so D because we broke it up into two seperate parts then singled the two out and when we put it back together it shows D

Answer 66

That's right. Might be a good idea to review our work so that you can be sure you know how to do it yourself. Another problem?

Thanks once again, roadjester!

Answer 67

No problem.

Answer 68

yes please I need to make good on this review or im dead when Monday roles around

Answer 69

I can help. Perhaps roadjester could also. But be forewarned: I'll need to leave my computer frequently, since I'm expecting a tow truck to arrive here soon. Please post your next question separately from this old post. Thx.

Answer 70

That doesnt sound good

Answer 71

There are plenty of potential helpers here on OpenStudy, Decarr, and you do have almost a day and a half left 'til Monday.