Find the domain and range of the function

y = 5 - square root of(9 - x^2)

i got the domain

But for the range, my work took a lot of space and came out to something weird. Can anyone work through this and show me how to get the range?

10. Let f(x) = square root of (3 - x).

Find an expression for f inverse x

I got that as y = 3 - x^2

But it says(Be sure to state any necessary domain restrictions???)

11. f(x) = cube root of (x + 2) and g(x) = xcubed - 2

True or false

a. g(x) = f inverse of x

i got as True

b. f of g of x = 1

i got as True

c. The function is one to one

Dont know how to prove this other than graphing and using vert line test

Is there easier way?

20. Express y as a function of x, given that the constant C is a positive number : e ^(y + C) = x^2 + 4

No idea ....lol never did this in last year class

23. Solve each equation without using a calc

a. 2lnx - ln3 = 2

b. ln(x - 2) + ln(x + 5) = 2ln3

For these two, i am not remembering something because these should be easy...im not seeing something here...