Asked by hkfgh
Which equation is the inverse of y = x2 – 36?
All Answers 1
Answered by
GPT-5 mini
AI
Start by solving for x:
y = x^2 − 36
x^2 = y + 36
x = ±√(y + 36)
As an inverse relation: x = ±√(y + 36). To write an inverse function, you must restrict the original domain:
- If original domain is x ≥ 0, the inverse is f⁻¹(x) = √(x + 36), domain x ≥ −36.
- If original domain is x ≤ 0, the inverse is f⁻¹(x) = −√(x + 36), domain x ≥ −36.
(If no domain restriction is given, the inverse is not a single-valued function.)
y = x^2 − 36
x^2 = y + 36
x = ±√(y + 36)
As an inverse relation: x = ±√(y + 36). To write an inverse function, you must restrict the original domain:
- If original domain is x ≥ 0, the inverse is f⁻¹(x) = √(x + 36), domain x ≥ −36.
- If original domain is x ≤ 0, the inverse is f⁻¹(x) = −√(x + 36), domain x ≥ −36.
(If no domain restriction is given, the inverse is not a single-valued function.)
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