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Find the inverse of the function.\newliney=−4x+4y = -4x + 4\newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney=y = ______

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Full solution

Q. Find the inverse of the function.\newliney=−4x+4y = -4x + 4\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=−4y+4x = -4y + 4.
  2. Solve for y: Next, we need to solve for y. To do this, we add 4y4y to both sides of the equation to get x+4y=4x + 4y = 4.
  3. Isolate terms with y: Now, we subtract xx from both sides to isolate the terms with yy on one side: 4y=4−x4y = 4 - x.
  4. Divide by 44: To solve for yy, we divide both sides of the equation by 44. This gives us y=4−x4y = \frac{4 - x}{4}.
  5. Simplify the equation: We can simplify the right side of the equation by dividing both terms by 44: y=1−(14)xy = 1 - \left(\frac{1}{4}\right)x.

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