Question

Determinati functia de gradul I, f:R->R pentru situatia:
f(x)=2x+2f(2)

Answer 1

f(x)=ax+b, f(2)=2a+b
ax+b=2x+4a+2b
ax-4a-b=2x
a=2
-4a-b=0, -8-b=0, b=-8
f(x)=2x-8

Answer 2

f(x)=2x+2f(2)

x=2 ⇒ f(2)=2·2+2f(2)⇒f(2)=4+2f(2)⇒ -4= 2f(2)-f(2)⇒
 
-4 = f(2) ⇒ f(2) =-4

f(x) = 2x +2·(-4) ⇒ f(x) = 2x - 8.