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.
[tex]y=(x-1)^{2} -4[/tex] [switch x with y, and y with x]
[tex]x=(y-1)^2-4[/tex] [add both sides by 4]
[tex]x+4=(y-1)^2[/tex] [square root both sides]
[tex]\sqrt{x+4} =y-1[/tex] [add both sides by 1]
[tex]\sqrt{x+4} +1=y[/tex]
[tex]f^-^1(x)=1+\sqrt{x+4}[/tex]
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.
