- #1

hammonjj

- 33

- 0

**Homework Statement :**

Define f: ℝ→ℝ by f(x)=x^2. Find f^-1(T) for each of the following:

(a) T = {9}

(b) T = [4,9)

(c) T = [-4,9]

**The attempt at a solution:**

So, the inverse of f should be f^-1(T)=+/-√(x). Therefor:

(a) f^-1(9)= +/- 3

(b) f^-1(4)= +/- 2, f^-1(5)= +/- √(5), f^-1(6)= +/- √(6), f^-1(7)= +/- √(7), f^-1(8)= +/- 2√(2)

(c) Assuming I did the above correct, I have no idea how to do this part because clearly √(x) is not going to have a real solution from [-4,-1]

Any help would be awesome! Thanks!

James