If $f:R\to R$ is defined by $f(x)=x^2-3$, find $f^{-1} (-1)$ If $f:R\to R$ is defined by $f(x)=x^2-3$, find $f^{-1} (-1)$
My Attempt :
 $$f(x)=x^2-3$$
$$y=x^2-3$$
Then how to proceed further? 

$$
 f\left( x \right) = x^{2} - 3
$$
The function has two $x$ values that map to $y = -1$.


$$
 \color{blue}{f^{-1}(y) = \sqrt{x+3}} \qquad \Rightarrow \qquad f^{-1}\left( -1 \right) = \sqrt{2}
$$
$$
 \color{red}{f^{-1}(y) = -\sqrt{x+3}}\qquad \Rightarrow \qquad f^{-1}\left(-1 \right) = -\sqrt{2}
$$


