Question

Find the inverse of the given function. F(x) = -1/2 √(x+3), x ≥ -3

Answer 1

The inverse of the function F(x) = -1/2 √(x+3), x ≥ -3, is G(x) = 4x2 - 3, with the domain x ≥ 0.

Step-by-step explanation:

To find the inverse of the function F(x) = -1/2 √(x+3), with the domain x ≥ -3, we need to swap the roles of x and y and solve for y. Following the steps for function inversion:

1. Let y = -1/2 √(x+3).
2. Swap x and y to get x = -1/2 √(y+3).
3. Multiply both sides by -2 to get -2x = √(y+3).
4. Square both sides to eliminate the square root, obtaining 4x2 = y + 3.
5. Finally, subtract 3 from both sides to isolate y, yielding y = 4x2 - 3.

Thus, the inverse function of F(x) is G(x) = 4x2 - 3, with the domain x ≥ 0.