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

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Full solution

Q. Find the inverse of the function.\newliney=4x+7y = 4x + 7\newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney = ______
  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+7x = 4y + 7.
  2. Solve for yy: Next, we need to solve for yy. To do this, we subtract 77 from both sides of the equation to isolate the term with yy. This gives us x−7=4y+7−7x - 7 = 4y + 7 - 7.
  3. Isolate yy: Simplifying the equation, we get x−7=4yx - 7 = 4y. Now we need to isolate yy by dividing both sides of the equation by 44.
  4. Final result: Dividing both sides by 44 gives us (x−7)/4=y(x - 7) / 4 = y, or y=(14)x−74y = (\frac{1}{4})x - \frac{7}{4}.

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