solve for x when x/x

[cpohlman]

This is the problem: f(x)=(x-.2)/(x+.5) Find the inverse. I know I have to solve for x, but I can't remember how to do that.

 

[ChaoticLlama]

replace x with f(x) and f(x) with x, then solve for x. That should make things a little easier.

 

[Unco]

This is the problem: f(x)=(x-.2)/(x+.5) Find the inverse. I know I have to solve for x, but I can't remember how to do that.

\(\displaystyle \mbox{ y = \frac{x - \frac{1}{5}}{x + \frac{1}{2}}}\)

Multiply both sides by \(\displaystyle \mbox{x + \frac{1}{2}}\) (note restriction in domain)

\(\displaystyle \mbox{ y\left(x + \frac{1}{2}\right) = x - \frac{1}{5}}\)

Distribute the left-hand side, group x terms to one side, and factor out x to solve for x.