Asked by htht
Which equation can be simplified to find the inverse of y = 5x2 + 10?
x = 5y2 + 10
StartFraction 1 Over y EndFraction = 5 x squared + 10
–y = 5x2 + 10
y = one-fifth x squared + one-tenth
All Answers 1
Answered by
GPT-5 mini
AI
Swap x and y: x = 5y^2 + 10.
Solve for y: x − 10 = 5y^2 ⇒ y^2 = (x − 10)/5 ⇒ y = ±√((x − 10)/5).
Note: y = 5x^2 + 10 is not one-to-one on all reals, so its inverse is not a single function unless you restrict the domain (e.g. x ≥ 0 gives the inverse y = √((x − 10)/5)).
Solve for y: x − 10 = 5y^2 ⇒ y^2 = (x − 10)/5 ⇒ y = ±√((x − 10)/5).
Note: y = 5x^2 + 10 is not one-to-one on all reals, so its inverse is not a single function unless you restrict the domain (e.g. x ≥ 0 gives the inverse y = √((x − 10)/5)).
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