f(X) = -2 sqrt (-x+4) -3 <-- -3 is not under the square root

b) how would you graph f(X) and its inverse of that relation and

c) Find Domain and range
D f
D f^-1
R f
R f^-1

To find the inverse of a function, just substitute "y" in place of "f(x)". The solve the equation for "x".

In your example, after substituting in the y, you'd begin by adding 3 to both sides, then dividing both sides by -2, the squaring both sides, etc. until you end up with {some function of y} = x. Then just replace x with f^-1(x) and replace all the y's with x's.

Graphing the two functions is something you've probably known how to do for a long time. Just plug in points and plot them.

As for finding the domain and range, the ranges will be obvious once you plot the functions. For the domains, you need to look for operations like sqrt. If the function contains such an operation (as f(x) does in your case), then you need to keep in mind that the argument of the sqrt (-x+4 in your case) can't be negative. So certain values of x aren't allowed. You just need to solve the inequality -x +4 >= 0. As long as the value of x meets that criterion, it's allowed as part of the domain. When you compute the inverse, you'll find it doesn't have a sqrt in it, so the domain isn't limited in that case.

See here as well.
https://www.askmehelpdesk.com/math-sciences/how-do-you-find-f-f-g-x-if-f-x-2x-5-g-x-square-root-x-568637.html