To find the inverse of the function [tex]\( f(x) = 3 - 14x \)[/tex], we need to follow these steps:
1. Rewrite the function in terms of [tex]\( y \)[/tex]:
[tex]\[ y = 3 - 14x \][/tex]
2. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[
y = 3 - 14x
\][/tex]
Subtract 3 from both sides:
[tex]\[
y - 3 = -14x
\][/tex]
Divide both sides by -14:
[tex]\[
x = \frac{3 - y}{14}
\][/tex]
3. Express the solution as the inverse function:
Replace [tex]\( y \)[/tex] with [tex]\( x \)[/tex] to denote the inverse function:
[tex]\[
f^{-1}(x) = \frac{3 - x}{14}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{A. \, f^{-1}(x) = \frac{3-x}{14}}
\][/tex]
