Question

Sabendo-se que f(x) = ax + b, que f(-1) = 4 e que f(2) = 7, calcule o valor de f(8)

Answer 1

Dada a função (função polinomial do 1ª grau):

$\mathsf{f\left(x\right)=ax+b}$

Substituindo as coordenadas indicadas na questão:

Coordenada 01:

$\mathsf{f\left(-1\right)=a\left(-1\right)+b=4}\\\mathsf{-a+b=4}$

Coordenada 02:

$\mathsf{f\left(2\right)=2a+b=7}\\\mathsf{2a+b=7}$

Resolvendo o sistema linear com 2 variáveis:

$\begin{cases}{-a+b=4\\2a+b=7}\end{cases}\\\\\\\mathsf{multiplicando\:a\:primeira\:equacao\:por\:2\:e\:somando\:com\:a\:segunda\:temos:}\\\\\mathsf{-2a+2a+2b+b=8+7}\\\\\mathsf{3b=8+7}\\\\\mathsf{3b=15}\\\\\mathsf{b=\dfrac{15}{3}}\\\\\mathsf{b=5}\\\\\\\\\mathsf{-a+b=4}\\\\\mathsf{a=b-4}\\\\\mathsf{a=5-4}\\\\\mathsf{a=1}$

Logo, a função sera:

$\mathsf{f\left(x\right)=ax+b}\\\\\mathsf{f\left(x\right)=x+5}$

Assim, o valor da função quando $\mathsf{x\:=\:8}$ sera:

$\mathsf{f\left(8\right)=8+5}\\\\\boxed{\boxed{\mathsf{f\left(8\right)=13}}} \: \: \checkmark$