Inverse functions question?

[super_chris1234]

Hi,

Given f(x)=x/1+x

I know to swap x with y, then solve for y:

y=x/1+x

Then I swapped y with x and x with y:

x=y/1+y

Then I solve as you would with any fraction:

(1+y)x=y(1+y)

But where I get confused is when I multiply out the y(1+y), I get

xy+x=y² +y

So, how would I tackle this problem from here?

Any help is greatly appreciated.

Thanks,

Chris

 

[lookagain]

Hi,

Given f(x)=x/(1+x)

I know to swap x with y, then solve for y:

y=x/(1+x)

Then I swapped y with x and x with y:

x=y/(1+y)

Then I solve as you would with any fraction:

(1+y)x=y(1+y) Incorrect. It must be (1 + y)x = y.

But where I get confused is when I multiply out the y(1+y), I get

xy+x=y² +y This is also incorrect, as it followed from your wrong step above.
It must be xy + x = y **.

So, how would I tackle this problem from here?

You're typing the expressions wrong by not using grouping symbols.
I showed them inserted in the quote box.


From there?

** xy + x = y

Get the terms with y in them on one side of the equation and the
ones without y on the other side:


xy + x - y = 0

xy - y = -x


Factor out a y:

y(x - 1) = -x


Now, you must solve for y in terms of x.

Continue...