Question

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11. Determinați a € R, dacă:
a) A(a, a?)e G,, unde f: R → R, f(x) = 2x +3;
b) A(a, - a) € G,, unde f: R → R, f(x) = ax – 2;
c) A(a, 1)e Gy, undef: R → R, f(x)=x2-1.

Answer 1

$\it a)\ \ f(x)=2x+3\ \ \ \ \ (*)\\ \\ A(a,\ a)\in Gf \Rightarrow f(a)=a \stackrel{(*)}{\Longrightarrow}2a+3=a \Rightarrow 2a-a=-3 \Rightarrow a=-3\\ \\ \\ b)\ \ f(x)=ax-2\ \ \ \ (*)\\ \\ A(a,\ -a)\in Gf \Rightarrow f(a)=-a \stackrel{(*)}{\Longrightarrow} a^2-2=-a \Rightarrow a^2+a-2=0 \Rightarrow \\ \\ \Rightarrow a^2+2a-a-2=0 \Rightarrow a(a+2)-(a+2)=0 \Rightarrow (a+2)(a-1)=0 \Rightarrow \\ \\ \Rightarrow \begin{cases} \it a+2=0 \Rightarrow a=-2\\ \\ \it a-1=0\ \Rightarrow \ a=1\end{cases}$