22. On its own, is not invertible because it's not one-to-one because it's periodic. For instance, we can always find more than one value of for which ; this happens when .
But we can restrict the domain so that it can become invertible. If we only allow values of within , for example, then each will only be associated with a single value of . This is how the standard inverse sine is defined. With (restricted domain of sine), we guarantee that (range). So the domain of the inverse is , and the range of the inverse is .
is not in this restricted domain. But still exists as long as we take the standard domain (the entire real line), and . But then because this is the only value of for which .
In short: and are NOT inverses of one another, but rather one is an imperfect inverse of the other.
Use the formula: y = a(1 + r)^t a is the initial amount r is the percent of interest in decimal form t is the time in years y is the money after t years
Substitute the values given in the problem into the equation: 400(1+0.02)^20 Use a calculator or solve manually Around 594.38