Question

i'm supposed to find the expression of the inverse function of this f(x)=(x-3)²-1 i did this f(x)=y <=> f^-1(y)=x <=> y=(x-3)²-1 now i must find the expression by x plz help me

Answer 1

\[ f(x)=(x-3)^2-1\]\[f(x)+1=(x-3)^2\]\[\pm\sqrt{f(x)+1}=x-3\]\[3\pm\sqrt{f(x)+1}=x\]

\[f^{-1}(x)=3\pm\sqrt{x+1}\]