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Find the inverse of the function.\newliney=−3x+9y = -3x + 9\newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney=y = ______

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Q. Find the inverse of the function.\newliney=−3x+9y = -3x + 9\newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney=y = ______
  1. Swap xx and yy: To find the inverse of the function, we first swap xx and yy. This gives us the equation x=−3y+9x = -3y + 9.
  2. Solve for y: Next, we need to solve for y. To do this, we add 3y3y to both sides of the equation to get x+3y=9x + 3y = 9.
  3. Isolate y terms: Now, we subtract xx from both sides to isolate the terms with yy on one side. This gives us 3y=9−x3y = 9 - x.
  4. Divide by 33: To solve for yy, we divide both sides of the equation by 33. This simplifies to y=9−x3y = \frac{9 - x}{3}.
  5. Further simplify: We can further simplify the equation by dividing both terms in the numerator by 33. This gives us y=3−x3y = 3 - \frac{x}{3}.
  6. Rewrite as ax+bax + b: Finally, to write the answer in the form ax+bax + b, we rewrite −x3-\frac{x}{3} as (−13)x(-\frac{1}{3})x. The inverse function is y=3−(13)xy = 3 - (\frac{1}{3})x, or equivalently, y=−(13)x+3y = - (\frac{1}{3})x + 3.

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