Question

dada a função f(x)=a.x+b, com a,b e R e a≠ 0, determine a e b, sabendo que f(-1)= - 2 e f(5)= -8

Answer 1

$\fbox{ \mathsf{f(x)=ax+b} }\\\\\\\mathsf{f(-1)=-2~\Rightarrow~-2=a\cdot(-1)+b~\Leftrightarrow~-a+b=-2~\Leftrightarrow~\underline{a-b=2}}\\\\\mathsf{f(5)=-8~\Rightarrow~-8=a\cdot5+b~\Leftrightarrow~\underline{5a+b=-8}}\\\\\\\begin{Bmatrix}\mathsf{a-b=2~~~~~~~~~(I)}\\\\\mathsf{5a+b=-8~~~~~~(II)}\end.\\\\\\\mathsf{(I)+(II)~\Rightarrow~6a=-6~\Leftrightarrow~\underline{a=-1}}\\\\\mathsf{(I)'~\Rightarrow~-1-b=2~\Leftrightarrow~1+b=-2~\Leftrightarrow~\underline{b=-3}}\\\\\\\therefore~~\mathsf{a=-1~~e~~b=-3}$

Answer 2

f(x) = a.x + b

f(-1) = a(-1) + b = -2

f(5) = a(5) + b = -8

a(-1) + b = -2  (1)
a(5) + b = -8   (2)

Multiplicando (1) por -1 e somando com (2), temos:

a(1) - b = 2
a(5) + b = -8
-----------------(+)
a(6) = -6

a = -6/6

a = -1

Substituindo a = -1 na equação (2), temos:

a(5) + b = -8
(-1)(5) + b = -8

-5 + b = -8

b = -8 + 5

b = -3


f(x) = -x - 3

Resposta: f(x) = -x - 3

Espero ter ajudado.