What equation serves as the inverse of the function y = 2x² + 8?

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To find the inverse of the function y = 2x² + 8, we need to follow these steps:

  1. Replace y with x: This is the first step in finding the inverse. The equation becomes:

    2. x = 2y² + 8

  2. Isolate y: We need to solve this equation for y. Start by moving 8 to the left side:

    3. x - 8 = 2y²

  3. Divide by 2: Next, we divide both sides by 2 to simplify:

    4. (x - 8)/2 = y²

  4. Take the square root: Finally, to solve for y, we take the square root of both sides. Remember that taking a square root yields both positive and negative solutions:

    5. y = ±√((x - 8)/2)

Thus, the inverse function is:

y = ±√((x – 8)/2)

It’s important to note that since the original function involves squaring, it is not one-to-one over all real numbers. Therefore, when we refer to the inverse, we typically consider only one branch of the square root function (either the positive or negative), depending on the specific context in which the inverse is used.

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