inverse of 'predict' function

Question

Using predict() one can obtain the predicted value of the dependent variable (y) for a certain value of the independent variable (x) for a

Answer 1

You just have to rearrange the regression equation, but as the comments above state this may prove tricky and not necessarily have a meaningful interpretation.

However, for the case you presented you can use:

(1/coef(model)[2])*(model$family$linkfun(30/50)-coef(model)[1])

Note I did the division by the x coefficient first to allow the name attribute to be correct.