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f (-42)=? if f (x^2 + yf (z)) = xf (x) + zf (y) , (2017)> 0

Source: 15th -b QEDMO problem 8 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

May 30, 2021
algebrafunctionalfunctional equation

Problem Statement

For a function f:R→Rf: R\to R , f(2017)>0 f (2017)> 0 as well as f(x2+yf(z))=xf(x)+zf(y)f (x^2 + yf (z)) = xf (x) + zf (y) for all x,y,z∈Rx,y,z \in R is known. What is the value of f(−42)f (-42)?
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