Need to be able to do all these (and then some) before exam tomorrow, any help whatsoever would be appreciated.

1. State domain and range of f(x) 2-|x-1|

2. f(x) =

{√(x-1) where x ≥ 1

{4 where x<1

Find f(a-1) in terms of a

2. Let g;[b,2] -> R where g(x) = 1 - x^2 , if b is the smallest real value of such that g has an inverse function, find b and inverse of g(x)

3. let f:S->R. f(x) = square root (4-x^20) and S be the set of all real values for x for which f(x) is defined. Let g:R->R, where g(x) = x^2 + 1

Find S and range of f and g.

4. Let 'a' be a positive number, let f:[2, infinite) -> R, f(x) = a - x and let g

-infinite, 1] ->R, g(x) = x^2 + a. Find all values of 'a' for which f(g(x)) and g(f(x)) are defined.

5. find implied domain of square root (x^2 -x-2) and implied domain for square root (x-3x^2)

6.Sketch this hybrid function (just want to know how to go about doing this)

f(x)=

{2x+6 where 0<2x≤2

{-x + 5 where =4≤x≤0

{=4 where x < -4