Answer:
Hello,
Step-by-step explanation:
The problem is that the inverse function is not a function but
an union of 2 functions.
[tex]y=(x+6)^2+1\ is\ the\ orignal\ function\ f(x).\\\\Inverting\ x\ and\ y\ gives: \ x=(y+6)^2+1\\\\(y+6)^2=x-1 \ nota\ bene\ x-1\geq 0 \\(y+6)^2-(x-1)=0\\\\((y+6)-\sqrt{x-1} ) * ((y+6)+\sqrt{x-1}) =0\\\\y=-6+\sqrt{x-1}-6\ or\ y=-6-\sqrt{x-1}\\[/tex]
For the fun
,[tex]f_1(x)= (x+6)^2+1=0\ if\ x<6\\f_1^{-1}(x)=-6-\sqrt{x-1} =0\ if\ x<6\\\\f_2(x)=(x+6)^2+1=0\ if\ x \geq 6\\\\f_2^{-1}(x)=-6+\sqrt{x-1} =0\ if\ x\geq 6\\[/tex]
