Răspuns:
Explicație pas cu pas:
2 · f (x) + 3 · f (1-x) = 4x-1
functia de gradul intai este de forma f(x) = ax + b
f(x) = ax + b
f(1 - x) = a(1 - x) + b = a - ax + b
2 · f (x) + 3 · f (1-x) = 2(ax + b) + 3(a - ax + b) = 2ax + 2b + 3a - 3ax + 3b
= -ax + 3a + 5b
-ax + 3a + 5b = 4x - 1
-a = 4
3a + 5b = -1
-------
a = -4
-12 + 5b = -1
5b = 12 - 1 = 11
b = 11/5
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f(x) = -4x + 11/5
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Verificare:
f(x) = -4x + 11/5
f(1 - x) = -4(1 - x) + 11/5 = -4 + 4x + 11/5 = 4x - 20/5 + 11/5 = 4x -9/5
2 · f (x) + 3 · f (1-x) = 2(-4x + 11/5) + 3(4x - 9/5)
= -8x + 22/5 + 12x - 27/5 = 4x - 5/5 = 4x - 1
