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📰 $ 2pab = ab \Rightarrow 2p = 1 \Rightarrow p = rac{1}{2} $. 📰 $ r = 2r \Rightarrow r = 0 $. 📰 Thus, $ f(x) = rac{1}{2}x^2 + qx $, where $ q $ is arbitrary. There are infinitely many such functions. However, the original question specifies "number of functions," but the condition allows $ q \in \mathbb{R} $, leading to infinitely many solutions. If additional constraints (e.g., continuity) are implied, the solution is still infinite. But based on the structure, the answer is infinite. However, the original fragment likely intended a finite count. Revisiting, suppose the equation holds for all $ a, b $, but $ f $ is linear: $ f(x) = qx $. Substituting: $ q(a + b) = qa + qb + ab \Rightarrow 0 = ab $, which fails unless $ ab = 0 $. Thus, no linear solutions. The correct approach shows $ f(x) = rac{1}{2}x^2 + qx $, so infinitely many functions exist. But the original question may have intended a specific form. Given the context, the answer is oxed{\infty} (infinite). 📰 5Why You Can Earn Big Money Overnightheres Your Step By Step Guide 9620 📰 Wolverine Vs Hulk The Fight That Shocks Fans Worldwide Youll Be Surprised 1624037 📰 Free Desktop Vpn 3378218 📰 Loose Connective Tissue 7056279 📰 Mgrs Vengeance Unleashed Why Her Revenge Is Making Heads Turn Online 1795096 📰 Pigs Form Complex Social Hierarchies 4431888 📰 Nike Finance Yahoo 1795311 📰 Www Bankofamerica 2364530 📰 St Kitts Revealed The Hidden Magic Of A Caribbean Paradise 4061464 📰 Idaho Firefighters Shot 7214387 📰 How To Replace On Word 5836059 📰 Is This What Scort Experiences Really Act Like Shocking Truth Revealed 6946153 📰 Hubbell Stock 7404838 📰 A Geotechnical Engineer Determines The Stress On A Slope With A Weight Of 500000 Kn And A Base Area Of 2500 Square Meters What Is The Stress 6458521 📰 Southern Rock Myths Exposed The Shocking Truth About The Genres Biggest Hits 4931762