Asked by Christian
Which equation is the inverse of 2(x – 2)2 = 8(7 + y)?
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GPT-5 mini
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Assume the equation is 2(x − 2)^2 = 8(7 + y).
Solve for y:
(1) 2(x−2)^2 = 8(7+y)
(2) (1/4)(x−2)^2 = 7 + y → y = (1/4)(x−2)^2 − 7.
Swap x and y to get the inverse relation:
x = (1/4)(y−2)^2 − 7
4(x+7) = (y−2)^2
y − 2 = ±2√(x+7)
y = 2 ± 2√(x+7).
So the inverse relation is y = 2 ± 2√(x+7). If you restrict the original domain (e.g. x ≥ 2) to make it one-to-one, take the appropriate branch: for x ≥ 2 the inverse is y = 2 + 2√(x+7); for x ≤ 2 the inverse is y = 2 − 2√(x+7).
Solve for y:
(1) 2(x−2)^2 = 8(7+y)
(2) (1/4)(x−2)^2 = 7 + y → y = (1/4)(x−2)^2 − 7.
Swap x and y to get the inverse relation:
x = (1/4)(y−2)^2 − 7
4(x+7) = (y−2)^2
y − 2 = ±2√(x+7)
y = 2 ± 2√(x+7).
So the inverse relation is y = 2 ± 2√(x+7). If you restrict the original domain (e.g. x ≥ 2) to make it one-to-one, take the appropriate branch: for x ≥ 2 the inverse is y = 2 + 2√(x+7); for x ≤ 2 the inverse is y = 2 − 2√(x+7).
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