1.18 Tapps exercise: how do i solve that for y?

OK, so you’re looking for the inverse function of $y=\frac{x}{\mathrm{2x}+1}$ and you come up with $x=\frac{y}{\mathrm{2y}+1}$ . Now you have to solve that for $y$ , and you’re stuck.

First of all, let’s review what that means! To “solve it for y” means that we have to get it in the form $y$ = something , where the something has no $y$ in it anywhere. So $y=\mathrm{2x}+4$ is solved for $y$ , but $y=\mathrm{2x}+\mathrm{3y}$ is not. Why? Because in the first case, if I give you $x$ , you can immediately find $y$ . But in the second case, you cannot.

“Solving it for $y$ ”is also sometimes called“isolating $y$ ”because you are getting $y$ all alone.

So that’s our goal. How do we accomplish it?

Ta-da! We’re done! $\frac{x}{1-\mathrm{2x}}$ is the inverse function of $\frac{x}{\mathrm{2x}+1}$ . Not convinced? Try two tests.

Test 1:

Test 2:

Now, you try it! Follow the above steps one at a time. You should switch roles at this point: the previous student should do the work, explaining each step to the previous teacher . Your job: find the inverse function of $\frac{x+1}{x-1}$ .