The value of $y$ is inversely proportional to $x^{2} − 3$ and $y = 1$ when $x = 1$. 

1. Express $y$ as a function of $x$.

   Hint (a):

   Find '$k$' and substitute back into the equation.

2. Write $y = f\left(x\right)$ and find $f\left(−3\right)$, $f\left(2\right)$, $f ( \frac { 1 } { 2 } )$, and $f ( - \frac { 1 } { a } )$.

   Partial Answer (b):

   $f\left(−3\right)=-\frac{1}{3}$