Find the inverse of the function. y = 4x + 7 Write your answer in the form ax + b. Simplify any fractions. y = ______

Swap x and y: To find the inverse of the function, we first swap x and y. This gives us the equation x = 4y + 7.Solve for y: Next, we need to solve for y. To do this, we subtract 7 from both sides of the equation to isolate the term with y. This gives us x - 7 = 4y + 7 - 7.Isolate y: Simplifying the equation, we get x - 7 = 4y. Now we need to isolate y by dividing both sides of the equation by 4.Final result: Dividing both sides by 4 gives us (x - 7) / 4 = y, or y = (1/4)x - 7/4.

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Find the inverse of the function. $\newline$ $y = 4x + 7$ $\newline$ Write your answer in the form $ax + b$ . Simplify any fractions. $\newline$ y = ______

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Algebra 1

Find the inverse of a linear function

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Q. Find the inverse of the function.

\newline

y = 4x + 7

\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 $x = 4y + 7$ .
Solve for $y$ : Next, we need to solve for $y$ . To do this, we subtract $7$ from both sides of the equation to isolate the term with $y$ . This gives us $x - 7 = 4y + 7 - 7$ .
Isolate $y$ : Simplifying the equation, we get $x - 7 = 4y$ . Now we need to isolate $y$ by dividing both sides of the equation by $4$ .
Final result: Dividing both sides by $4$ gives us $(x - 7) / 4 = y$ , or $y = (\frac{1}{4})x - \frac{7}{4}$ .