Inverse functions (1 Viewer)

[steve001]

Hey, i cant rearrange these two functions in order to just switch the x and y to get the inverse. The two equations are:

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

Thanks in advance

 

[azureus88]

quadratic formula would be useful.

 

[scardizzle]

Hey, i cant rearrange these two functions in order to just switch the x and y to get the inverse. The two equations are:

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

Thanks in advance

you have to complete the square for 2

x = y + 1/y

xy = y^2 + 1

y^2 - xy = -1

(y - x/2)^2 - x^2/4 = -1

y-x/2 = (x^2/4-1)^1/2

y = (x^2/4 -1)^1/2 + x/2

1. is similar but a bit more messy you have to factorise x before completing the square

 

[jet]