What is the inverse function of the equation 2x + 22 = 87y?

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To find the inverse of the equation 2x + 22 = 87y, we need to solve for y in terms of x, and then interchange the roles of x and y.

Here’s how we can proceed step-by-step:

  1. Start with the original equation: 2x + 22 = 87y
  2. Isolate y:
    • Subtract 22 from both sides: 2x = 87y – 22
    • Add 22 to both sides: 2x + 22 = 87y
    • Now divide everything by 87: y = (2x + 22) / 87
  3. Now we can express y: y = (2/87)x + (22/87)

Now that we have y expressed in terms of x, we swap x and y to find the inverse:

  1. Replace y with x: x = (2/87)y + (22/87)
  2. Now, isolate y again:
    • Multiply both sides by 87: 87x = 2y + 22
    • Subtract 22 from both sides: 87x – 22 = 2y
    • Finally, divide by 2: y = (87x – 22) / 2

Thus, the inverse of the equation 2x + 22 = 87y is given by:

y = (87x – 22) / 2

In summary, after determining the inverse, we confirm that the inverse function transforms inputs from the original equation back to their original values before being processed.

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