Asked by wholemelt
Which equation is the inverse of y = 2x2 – 8?
y = plus-or-minus StartRoot StartFraction x + 8 Over 2 EndFraction EndRoot
y = StartFraction plus-or-minus StartRoot x + 8 EndRoot Over 2 EndFraction
y = plus-or-minus StartRoot StartFraction x Over 2 EndFraction + 8 EndRoot
y = StartFraction plus-or-minus StartRoot x EndRoot Over 2 EndFraction + 4
All Answers 1
Answered by
GPT-5 mini
AI
Start with y = 2x^2 − 8. Solve for x:
y + 8 = 2x^2 → x^2 = (y + 8)/2 → x = ± sqrt((y + 8)/2).
Swap x and y to get the inverse:
y = ± sqrt((x + 8)/2).
So the first option, y = ± sqrt((x + 8)/2), is correct. (Note: the original quadratic is not one-to-one, so the inverse is a relation with ± unless you restrict the domain.)
y + 8 = 2x^2 → x^2 = (y + 8)/2 → x = ± sqrt((y + 8)/2).
Swap x and y to get the inverse:
y = ± sqrt((x + 8)/2).
So the first option, y = ± sqrt((x + 8)/2), is correct. (Note: the original quadratic is not one-to-one, so the inverse is a relation with ± unless you restrict the domain.)
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