Find the inverse of the one-to-one function.
\[
f(x)=-3 x-6
\]
\[
f^{-1}(x)=
\]
(A)
\[
\frac{x-6}{-3}
\]
\[
f^{11}(x)=
\]
(B)
\[
\frac{-3 x+6}{-3}
\]
\[
f^{7}(x)=
\]
(C)
\[
\frac{y+6}{-3}
\]
$f^{\prime}(x)=$
(D)
\[
\frac{x+6}{-3}
\]

Answer

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Answer

$\boxed{f^{-1}(x) = \frac{x+6}{-3}}$

Steps

Step 1 ：Given function: $f(x) = -3x - 6$

Step 2 ：Replace $f(x)$ with y: $y = -3x - 6$

Step 3 ：Swap x and y: $x = -3y - 6$

Step 4 ：Solve for y: $y = \frac{x+6}{-3}$

Step 5 ：$\boxed{f^{-1}(x) = \frac{x+6}{-3}}$