Va rog frumos sa ma ajutati si pe mn...rezolvati va rog problema asta

Fie f:R->R, f(x) = ax + b, o functie de gradul intai.Un punct M(a,b) apartine graficului functiei daca f(a) = b.

A(1, 2)∈Gf => f(1)=2 => a+b=2

B(-2,1)∈Gf => f(-2)=1 => -2a+b=1

a=2-b => -2(2-b)+b=1 => -4+2b+b=1 > 3b = 5 => b = 5/3 => a = 1/3

[tex]f(x) = \frac{1}{3}x + \frac{5}{3} [/tex]

Functia a fost determinata.

[tex] f: \mathbb{R}\to \mathbb{R}~~~,f(x) = ax+b \\ \\
A(1;2) \in Gf \Rightarrow f(1) = 2 \\
~~~~~~~~~~~~~~~~~~~~~f(1) = a+b~ \boxed{\Rightarrow a+b = 2} \\ \\
B(-2;1) \in Gf \Rightarrow f(-2) = -1 \\
~~~~~~~~~~~~~~~~~~~~~f(-2) = -2a+b~ \boxed{\Rightarrow -2a+b = -1}

\left \{ {{a+b=2}~~\cdot |(-1) \atop {-2a+b=-1}} \right. \\ \\
\left \{ {{-a-b=-2} \atop {-2a+b=-1}} \right. \\
-3a=-3 \Rightarrow \boxed{a= 1} \\ \\
-a-b = -2 \Rightarrow \boxed{b=1} \\ \\
\boxed{f(x)=1 \cdot x+1} \\ \\
\boxed{f(x)=x+1} [/tex]