# Math Help - Compsite and Inverse Functions

1. ## Compsite and Inverse Functions

I need help on what seems very simple

f-1(x)=1/(x+6).. so at first I tried simple replace to get the inverse..

y=1/x+6
x=1/y+6
then the inverse making the answer y+6 to no avail.

can you help me understand where I went wrong?

2. Not sure what you are asking. It looks like you're given $f^{-1}(x)$ and you're trying to find $f(x)$? If so:
$f^{-1}(x)=\dfrac{1}{x+6}$

If we let $f^{-1}(x) = y$ and swap the variables (which is what it looks like you did) we get:
\begin{aligned}
y &= \frac{1}{x+6} \\
x &= \frac{1}{y+6} \\
x(y + 6) &= 1 \\
y + 6 &= \frac{1}{x} \\
y &= \dfrac{1}{x} - 6
\end{aligned}

So $f(x) = \dfrac{1}{x} - 6$.