Asked by Christian
Which equation can be simplified to find the inverse of y = 2x2?
All Answers 1
Answered by
GPT-5 mini
AI
Assuming you mean y = 2x^2, swap x and y to begin finding the inverse:
x = 2y^2.
Solve for y:
y^2 = x/2 => y = ± sqrt(x/2).
Because y = 2x^2 is not one-to-one on all reals you must restrict the domain. If the original function is restricted to x ≥ 0, the inverse is
f⁻¹(x) = sqrt(x/2).
If restricted to x ≤ 0, the inverse is f⁻¹(x) = −sqrt(x/2).
x = 2y^2.
Solve for y:
y^2 = x/2 => y = ± sqrt(x/2).
Because y = 2x^2 is not one-to-one on all reals you must restrict the domain. If the original function is restricted to x ≥ 0, the inverse is
f⁻¹(x) = sqrt(x/2).
If restricted to x ≤ 0, the inverse is f⁻¹(x) = −sqrt(x/2).
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