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Find the inverse of the function.\newliney=−2x+9y = -2x + 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=−2x+9y = -2x + 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=−2y+9x = -2y + 9.
  2. Solve for y: Next, we need to solve for yy. To do this, we add 2y2y to both sides of the equation to get x+2y=9x + 2y = 9.
  3. Isolate terms with yy: Now, we subtract xx from both sides to isolate the terms with yy on one side. This gives us 2y=9−x2y = 9 - x.
  4. Divide by 22: To solve for yy, we divide both sides of the equation by 22. This simplifies to y=9−x2y = \frac{9 - x}{2}.
  5. Rewrite in ax+bax + b form: We can rewrite (9−x)/2(9 - x) / 2 as (−1/2)x+9/2(-1/2)x + 9/2 to match the form ax+bax + b.

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