If $y$ varies inversely as $x$, then $y=\frac{k}{x}$.

$y=\frac{k}{x+6}$

Use the fact that $y=1$ when $x=1$ to solve for $k$.

Substitute $k$ back into your original equation.
To write $y$ as a function of $x$, change $y=$ to $f(x)=$ .