Great Question!
The problem we have at hand is known to be a function, which maps elements from one set of objects, ( the domain ) onto another, the range. If we were to consider an ordered pair, say ( x, y ), then the function would map x onto y. The inverse function is simply the reverse. Take the ordered pair (-4,0). Function g would map - 4 onto 0, such that . Therefore, the inverse function would map 0 onto - 4, resulting in
. And there you have it! Our first part is answered!
____
This second bit here is interesting. Let -
- Switch x and y,
- And now solve this equation for y,
As you can see, we have taken the inverse of h( x ). As y = h( x ), we can thus conclude the following -
____
The composition (h^-1 o h)(-5) is, in other words, h^-1(h(-5)). We can therefore calculate h(-5) and then take it's inverse -
Now we can take it's inverse -
Our solution for this last bit is - 5. And, if you don't feel like reading through this entire explanation just take a look at the " summed up " answer below,
I do hope that helps you!