Asked by htht
hich 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
Solve for x, then swap variables (or swap and solve):
y = 2x^2 − 8
Swap x and y: x = 2y^2 − 8
x + 8 = 2y^2
y^2 = (x + 8)/2
y = ± sqrt((x + 8)/2)
So the correct choice is the first one: y = ± sqrt((x + 8)/2). (If you want a true function inverse, restrict the domain of the original to x ≥ 0 or x ≤ 0 to take only the + or − branch.)
y = 2x^2 − 8
Swap x and y: x = 2y^2 − 8
x + 8 = 2y^2
y^2 = (x + 8)/2
y = ± sqrt((x + 8)/2)
So the correct choice is the first one: y = ± sqrt((x + 8)/2). (If you want a true function inverse, restrict the domain of the original to x ≥ 0 or x ≤ 0 to take only the + or − branch.)
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