Question

Determinati a apartine R stiind ca:
a)f:{-2;1;2;3}->R,f(x)=ax-2 si A(1;-1) apartine Gf
b)f:{-2;-1;1;2}->R,f(x)=3x+a si A(1;-1)apartineGf
c)f:{-3;-1;1;2}->R,f(x)=ax-5 si A(2;-1) apartine Gf

Answer 1

a) Observam ca abscisa punctului A, adica x=1, se afla in domeniul de defintie al functiei f. Daca A∈Gf ⇒f(1)=-1 . Inlocuim x=1 in f(x)=ax-2. Deci f(1)=a-2 si punem conditia  f(1)=-1 ⇒a-2=-1⇒a=2-1 ⇒a=1. Verificam  ca A∈Gf pentru a=1.
f(x)=x-2 ⇒ f(1)= 1-2 = -1 . Corect; coordonatele punctului A indeplinesc conditiile.
b) Idem: A(1;-1)∈Gf ⇒ f(1)=-1 ⇒pt x=1, 3x+a=-1 ⇒3+a=-1 ⇒a=-4. Verificam f(x)=3x-4  f(1)=3-4=-1. Corect.
c)Idem: A(2;-1)∈Gf ⇒ f(2)=-1 ⇒ax-5=-1 ⇒2a-5=-1 ⇒2a=4 ⇒a=2.  Verificam:
f(x)=2x-5  f(2)=2·2-5=4-5=-1 Corect.