inverse image under ring homomorphism

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Hi there!

Just starting to learn Sage and can't get why both inverse_image calls below give an error saying the given element does not have a preimage, while y^2 clearly has xbar as preimage.

Referring to the generators of R1 and R2 explicitly doesn't help either.

sage: R.<x, y> = QQ[]
sage: R1 = R.quotient(R.ideal(y^2 - x^3))
sage: R2 = R.quotient(R.ideal(x))
sage: h = R1.hom([y^2, y^3], R2)
sage: h
Ring morphism:
  From: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (-x^3 + y^2)
  To:   Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x)
  Defn: xbar |--> y^2
        ybar |--> y^3

sage: h.inverse_image(y)
Traceback (most recent call last)
...
ValueError: element y does not have preimage

sage: h.inverse_image(y^2)
Traceback (most recent call last)
...
ValueError: element y^2 does not have preimage

Thanks!