Question

consider the following function.
f(x)=x^2-8, x less than or equal to 0. Find the inverse of f(x)

Answer 1

let f(x)=y
y=x^2-8
x^2=y+8
\[x=-\sqrt{y+8},\]
interchange x and y
\[y=-\sqrt{x+8},or f ^{-1}\left( x \right)=-\sqrt{x+8}\]

Answer 2

why is x= -sqrt (y+8). Negative? @surjithayer