Find the inverse function of $f$ informally.
\[
\begin{array}{l}
f(x)=5 x+9 \\
f^{-1}(x)=
\end{array}
\]

Answer

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Answer

$\boxed{f^{-1}(x) = \frac{x - 9}{5}}$

Steps

Step 1 ：$y = 5x + 9$

Step 2 ：$x = 5y + 9$

Step 3 ：$x - 9 = 5y$

Step 4 ：$y = \frac{x - 9}{5}$

Step 5 ：$f^{-1}(x) = \frac{x - 9}{5}$

Step 6 ：$f^{-1}(f(x)) = \frac{5x + 9 - 9}{5} = x$

Step 7 ：$\boxed{f^{-1}(x) = \frac{x - 9}{5}}$