Finding inverse functions when there is X^2+x

  • #1

Homework Statement



f(x)= 2x + x^2

Homework Equations





The Attempt at a Solution



I don't know how to make x the subject
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement



f(x)= 2x + x^2

Homework Equations





The Attempt at a Solution



I don't know how to make x the subject

You need to solve for x in the equation x^2 + 2x = y. This is a simple quadratic equation.
 
  • #3
You need to solve for x in the equation x^2 + 2x = y. This is a simple quadratic equation.

Okay thank you!

I've got it:

X^2 +2x = y

add one so you get a quadratic that has a "squared"

x^2 +2x +1 = y + 1

solve quadratic:

(x+1)^2 = y + 1

x = (y+1)^-1/2 -1

f-1(x) = (x+1)^-1/2 -1

:)
 
Last edited:
  • #4
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Okay thank you!

I've got it:

X^2 +2x = y

add one so you get a quadratic that has a "squared"

x^2 +2x +1 = y + 1

solve quadratic:

(x+1)^2 = y + 1

x = (y+1)^-1/2 -1
No.
Starting from two lines above, you want to solve for x.
When you do this, don't forget that you need ± in there somewhere.
f-1(x) = (x+1)^-1/2 -1

:)
Note that the equation y = x2 + 2x does not give y as a 1-to-1 function of x, so there is no inverse function, unless you place restrictions on the domain.
 
  • #5
237
5
f-1(x) = (x+1)^-1/2 -1

:)
You have raised to the power -1/2. Where did the negative sign come from?
 
  • #6
You have raised to the power -1/2. Where did the negative sign come from?

Sorry, mistake when I was typing! Thank you for pointing it out
 

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