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Laviniacx
a fost răspuns

Determinati functia de gradul I, cu f:R -> R stiind ca:
f(x+1) =3(x+1) - 2f(1)
Determinati functiile de gradul I, f:R-> R, in urm cazuri:
a) f(x + 2) = 5x + 11
b) f(x)= 2x + 2f(2)
VA ROG MULT. MULTUMESC!

Răspuns :

f:R R
f(x)=ax+b
f(x+1)=ax+a+b
f(1)=a+b
ax+a+b=3x+3-2a-2b
ax=3x
a=3
a+b=3-2a-2b
b+2b=-3•3+3
3b=-6
b=-2
f(x)=3x-6
verif
3(x+1)-6=3x+3-6
2)a)f(x)=ax+b
f(x+2)=ax+2a+b=5x+11
ax=5x
a=5
10+b=11
b=1
f(x)=5x+1
b)f(x)=ax+b
f(2)=2a+b
ax+b=2x+4a+2b
a=2
b-2b=4•2
-b=8

b=-8
f(x)=2x-8

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