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Adi3
 one year ago
Will medal
Please help.
consider f(x) = 2x+1/x+3.
Find f^1(x)
Adi3
 one year ago
Will medal Please help. consider f(x) = 2x+1/x+3. Find f^1(x)

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Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2So first you want to set your function as y =...

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Alright now multiply x by y+3 to create a linear function.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2What do you get with that.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2\[x=\frac{2y+1}{y+3} \qquad xy +3x = 2y+1\] Do you see how this is working out?

Adi3
 one year ago
Best ResponseYou've already chosen the best response.0xy+3x=2y+1, how did you do this

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2\[(y+3) \cdot x= \frac{2y+1}{y+3}\cdot (y+3) \]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Then subtract 2y from both sides of the equation. \[xy2y+3x=1\] And then youd subtract 3x from both sides of the equation. \[xy2y=13x\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2because 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.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Now we factor out a y from the left hand side of the equation. What do you end up with when you do that?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2now we divide both sides of the equation by (x2) to solve for y. what is your equation then?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2careful with your signs. When you divide both sides by (x2) it doesnt change to (x+2)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2\[y(x2) = 13x\qquad \implies \qquad y=\frac{13x}{x2}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2now all you have to do is rewrite y as f\(^{1}\)(x) and this is your inverse function.
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