Question

dada a funçao afim f(x)=a+x+b sendo f(2)=-3,f(4)=9 f(11).

Answer 1

Toda função afim possui a forma:

$f(x) = ax + b$

Logo:

$f(2) = -3 \to f(2) = 2a + b \to \boxed{ 2a + b = -3} \\ \\ f(4) =9 \to f(4) = 4a + b \to \boxed{4a + b = 9}$

Assim:

$\left \{ {{2a+b=-3} \atop {4a + b = 9}} \right. \\ \\ (2-4)a + (1-1)b = -3 - 9 \\ -2a = -12 \\ \boxed{a = 6} \\ \\ b = 9 - 4a \\ b = 9 - 4*6 \\ b = 9 -24 \\ \boxed{b = -15}$

Logo temos:

$f(x) = 6x - 15 \\ \\ f(11) = 6*11 - 15 \\ \\ f(11) = 66 - 15 \\ \\ \boxed{f(11) = 51}$