Finding inverse functions when there is X^2+x

[applestrudle]

Homework Statement

f(x)= 2x + x^2

Homework Equations

The Attempt at a Solution

I don't know how to make x the subject

 

[Ray Vickson]

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.

 

[applestrudle]

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

:)

 

[Mark44]

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.

 

[skiller]

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

:)

You have raised to the power -1/2. Where did the negative sign come from?

 

[applestrudle]

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