Question

Does anyone know how to do this? I’m lost

Answer 1

Answer: B

Step-by-step explanation:

To find the inverse function, you switch x with y and y with x. Then, you solve for y.

$y=(x-1)^{2} -4$                                  [switch x with y, and y with x]                        

$x=(y-1)^2-4$                                  [add both sides by 4]

$x+4=(y-1)^2$                                  [square root both sides]

$\sqrt{x+4} =y-1$                                    [add both sides by 1]

$\sqrt{x+4} +1=y$

$f^-^1(x)=1+\sqrt{x+4}$

Now that we know the inverse function, we can actually tell that the answer is B. We know this because of the restriction that f(x) is x≤1. This makes it positive, and B the answer.