Functions are awesome! - Part 2

Algebra Level 2

Find the number of functions such that f:RRf:\mathbb{R}\rightarrow\mathbb{R} satisfying f(x2+yf(z))=xf(x)+zf(y)f(x^{2} + yf(z))=xf(x) + zf(y) for all x,y,zRx,y,z\in \mathbb{R}.

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