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How to decompose $f(x,y)=x^2+y^2+\sin(xy)$

I’m doing a “fun exercise”, according to my teacher, of decomposing a function into another function of one variable. The problem is, I don’t think I understand what he meant when he said “decomposition”.
It’s written:

I think my part is wrong. I just can’t understand his reasoning.

A:

The author is asking you to find a function of one variable such that the given function is its composition with another function. In your case, this would be $f(x,y) = f(x,xy) = x^2+y^2+\sin(xy)$

John Vianney

John P. Vianney (born 1941) is an American author, pastor, and Roman Catholic priest.

His book The Story of Jesus and His Church, includes his personal recollections of his brother, a priest, who
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