### Home > PC > Chapter 7 > Lesson 7.2.2 > Problem7-57

7-57.

If $y$ varies inversely as $x + 6$ and $y = 1$ when $x = 1$, complete the following problems.

1. Express y as a function of $x$, $y = f\left(x\right)$.

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 $f\left(x\right) =$.

2. Find $f\left(−3\right)$, $f\left(0\right)$, $f(\frac { 1 } { 3 })$, and $f(\frac { 1 } { a })$.

$f\left ( \frac{1}{a} \right )=\frac{7a}{1+6a}$