Problem

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The function $f$ represents $y$ in terms of $x$. If $f(x)=3-5 x$, determine the formula that reverses this process and gives $x$ in terms of $y$.
\[
\begin{array}{l}
x=\frac{y+3}{5} \\
x=3+5 y \\
x=\frac{1}{3-5 y} \\
x=\frac{y-3}{-5}
\end{array}
\]

Answer

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Answer

\(\boxed{x = \frac{y-3}{-5}}\) is the formula that reverses the process and gives $x$ in terms of $y$.

Steps

Step 1 :The function $f$ represents $y$ in terms of $x$. If $f(x)=3-5 x$, we are asked to determine the formula that reverses this process and gives $x$ in terms of $y$.

Step 2 :The question is asking for the inverse of the function $f(x) = 3 - 5x$. To find the inverse of a function, we swap $x$ and $y$ and solve for $y$. In this case, we will swap $x$ and $y$ in the equation $y = 3 - 5x$ and solve for $x$.

Step 3 :By swapping $x$ and $y$ in the equation $y = 3 - 5x$, we get $x = 3 - 5y$.

Step 4 :However, this is not in the form of $x$ in terms of $y$. We need to rearrange this equation to get $x$ on one side.

Step 5 :By rearranging the equation $x = 3 - 5y$, we get $x = \frac{y-3}{-5}$.

Step 6 :\(\boxed{x = \frac{y-3}{-5}}\) is the formula that reverses the process and gives $x$ in terms of $y$.

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