Question

The domain and f^1(x)

Answer 1

B

To solve for the inverse, just swap the x and y and solve for the new y.

$y=\sqrt{x} -8$

$x=\sqrt{y}-8$

$x+8=\sqrt{y}$

$(x+8)^2=y$

Then inspect both functions for the domain.

In the original function, x has to be greater than or equal to 0 or else you would have a negative square root which is impossible.

The inverse function has no limitations as any x could make that true.

The main things that will limit domain is square root of negative or divide by zero.

Therefore, x>=0 is the only domain restriction.