Okay so I have what seems to be a fairly simple problem. Find the domain and range of f(x)=(e^x) - 1. Then find the inverse and its domain and range.
Normally I can do this, but because of e I'm stuck.
dom f = R (you should already know this). To find the range of any function you should first draw a graph. It will then be clear that Ran f = (-1, +oo).
The rule for the inverse function is found by solving . If you're familiar with logarithms (and I assume you are since you've been set this problem) this equation should be easy to solve. Where do you get stuck?
Finally, you should know that and .
The domain and range of are all real numbers and all real numbers larger than 0, respectively. That is, in x can be any number and y can be any positive number. Now what about ? If you can calculate for any value of x, can't you then subtract 1 from any number? If can be any positive number and then you subtract 1 from it what do you get?