Find the inverse of the function. y = -3x + 9 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 = -3y + 9.Solve for y: Next, we need to solve for y. To do this, we add 3y to both sides of the equation to get x + 3y = 9.Isolate y terms: Now, we subtract x from both sides to isolate the terms with y on one side. This gives us 3y = 9 - x.Divide by 3: To solve for y, we divide both sides of the equation by 3. This simplifies to y = (9 - x) / 3.Further simplify: We can further simplify the equation by dividing both terms in the numerator by 3. This gives us y = 3 - x/3.Rewrite as ax + b: Finally, to write the answer in the form ax + b, we rewrite -x/3 as (-1/3)x. The inverse function is y = 3 - (1/3)x, or equivalently, y = - (1/3)x + 3.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the inverse of the function. $\newline$ $y = -3x + 9$ $\newline$ Write your answer in the form $ax + b$ . Simplify any fractions. $\newline$ $y =$ ______

View step-by-step help

Home

Math Problems

Algebra 1

Find the inverse of a linear function

Full solution

Q. Find the inverse of the function.

\newline

y = -3x + 9

\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 $x = -3y + 9$ .
Solve for y: Next, we need to solve for y. To do this, we add $3y$ to both sides of the equation to get $x + 3y = 9$ .
Isolate y terms: Now, we subtract $x$ from both sides to isolate the terms with $y$ on one side. This gives us $3y = 9 - x$ .
Divide by $3$ : To solve for $y$ , we divide both sides of the equation by $3$ . This simplifies to $y = \frac{9 - x}{3}$ .
Further simplify: We can further simplify the equation by dividing both terms in the numerator by $3$ . This gives us $y = 3 - \frac{x}{3}$ .
Rewrite as $ax + b$ : Finally, to write the answer in the form $ax + b$ , we rewrite $-\frac{x}{3}$ as $(-\frac{1}{3})x$ . The inverse function is $y = 3 - (\frac{1}{3})x$ , or equivalently, $y = - (\frac{1}{3})x + 3$ .