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Find the inverse of the function. $\newline$ $y = -2x + 6$ $\newline$ Write your answer in the form $ax + b$ . Simplify any fractions. $\newline$ $y =$ ______

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Find the inverse of a linear function

Full solution

Q. Find the inverse of the function.

\newline

y = -2x + 6

\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 $x = -2y + 6$ .
Solve for y: Next, we need to solve for y. To do this, we add $2y$ to both sides of the equation to get $x + 2y = 6$ .
Isolate terms with $y$ : Now, we subtract $x$ from both sides to isolate the terms with $y$ on one side: $2y = 6 - x$ .
Divide by $2$ : To solve for $y$ , we divide both sides of the equation by $2$ . This gives us $y = \frac{6 - x}{2}$ .
Distribute division: We can simplify the equation further by distributing the division across the terms in the numerator: $y = \frac{6}{2} - \frac{x}{2}$ .
Simplify and rewrite: Simplifying the fractions gives us $y = 3 - \frac{1}{2}x$ . To write it in the form $ax + b$ , we rewrite it as $y = -\frac{1}{2}x + 3$ .

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