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Find the inverse of the function. $\newline$ $y = -2x + 8$ $\newline$ 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 + 8

\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 $x = -2y + 8$ .
Add and isolate terms: Next, we need to solve for $y$ . To do this, we'll add $2y$ to both sides of the equation to get $x + 2y = 8$ .
Divide by $2$ : Now, we subtract $x$ from both sides to isolate the terms with $y$ on one side. This gives us $2y = 8 - x$ .
Distribute division: To solve for $y$ , we divide both sides of the equation by $2$ . This simplifies to $y = \frac{8 - x}{2}$ .
Simplify fractions: We can further simplify the equation by distributing the division across the terms in the numerator. This gives us $y = \frac{8}{2} - \frac{x}{2}$ .
Rewrite in desired form: Simplifying the fractions, we get $y = 4 - \left(\frac{1}{2}\right)x$ . To match the form $ax + b$ , we rewrite this as $y = -\left(\frac{1}{2}\right)x + 4$ .

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