Adi3
  • Adi3
Will medal Please help. consider f(x) = 2x+1/x+3. Find f^-1(x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Adi3
  • Adi3
@dan815
Jhannybean
  • Jhannybean
So first you want to set your function as y =...
Adi3
  • Adi3
ok so 2y+1/y+3 = x

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Adi3
  • Adi3
then
Jhannybean
  • Jhannybean
Alright now multiply x by y+3 to create a linear function.
Jhannybean
  • Jhannybean
What do you get with that.
Adi3
  • Adi3
xy+3x
Jhannybean
  • Jhannybean
\[x=\frac{2y+1}{y+3} \qquad xy +3x = 2y+1\] Do you see how this is working out?
Adi3
  • Adi3
xy+3x=2y+1, how did you do this
Adi3
  • Adi3
ohh did u cross muliply
Jhannybean
  • Jhannybean
\[(y+3) \cdot x= \frac{2y+1}{y+3}\cdot (y+3) \]
Jhannybean
  • Jhannybean
Yes.
Adi3
  • Adi3
ok, then
Jhannybean
  • Jhannybean
Then subtract -2y from both sides of the equation. \[xy-2y+3x=1\] And then youd subtract -3x from both sides of the equation. \[xy-2y=1-3x\]
Jhannybean
  • Jhannybean
Following?
Adi3
  • Adi3
why did -3x switch?
Jhannybean
  • Jhannybean
because we want to isolate all the terms with `y` to the left side of the equation, and 3x does not have a `y` so we send it to the other side. In the process of solving for inverse functions, we switch x and y, then resolve for y.
Adi3
  • Adi3
ohhh ok, what to do next
Jhannybean
  • Jhannybean
Now we factor out a y from the left hand side of the equation. What do you end up with when you do that?
Adi3
  • Adi3
y(x-2)
Jhannybean
  • Jhannybean
Good.
Jhannybean
  • Jhannybean
now we divide both sides of the equation by (x-2) to solve for y. what is your equation then?
Adi3
  • Adi3
1-3x/x+2
Jhannybean
  • Jhannybean
careful with your signs. When you divide both sides by (x-2) it doesnt change to (x+2)
Jhannybean
  • Jhannybean
\[y(x-2) = 1-3x\qquad \implies \qquad y=\frac{1-3x}{x-2}\]
Adi3
  • Adi3
Thank you.
Jhannybean
  • Jhannybean
now all you have to do is rewrite y as f\(^{-1}\)(x) and this is your inverse function.

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