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Find the inverse of the function. $\newline$ $y = -2x + 1$ $\newline$ Write your answer in the form $ax + b$ . Simplify any fractions. $\newline$ $y =$ ______

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Find the inverse of a linear function

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Q. Find the inverse of the function.

\newline

y = -2x + 1

\newline

Write your answer in the form

ax + b

. Simplify any fractions.

\newline

y =

______

Swap $x$ and $y$ : To find the inverse of the function, we first swap $x$ and $y$ . This gives us the equation $x = -2y + 1$ .
Add and isolate $y$ : Next, we need to solve for $y$ . To do this, we'll add $2y$ to both sides of the equation to get $x + 2y = 1$ .
Divide by $2$ : Now, we subtract $x$ from both sides to isolate the term with $y$ on one side: $2y = 1 - x$ .
Simplify numerator: To solve for $y$ , we divide both sides of the equation by $2$ . This gives us $y = \frac{1 - x}{2}$ .
Rearrange terms: We can simplify this further by distributing the division across the terms in the numerator: $y = \frac{1}{2} - \frac{x}{2}$ .
Rearrange terms: We can simplify this further by distributing the division across the terms in the numerator: $y = \frac{1}{2} - \frac{x}{2}$ .Finally, we can write the inverse function in the form $ax + b$ by rearranging the terms: $y = -\frac{1}{2}x + \frac{1}{2}$ .

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