Question

A função f é definida por f(x)=ax+b, sabendo-se que f(-1)=3 e f(3)=1, podemos afirmar que f(1) é: *

0

-3

3

2

-2

Answer 1

$\Large\boxed{\begin{array}{l}\sf f(x) =ax+b\\\sf f(-1)=a\cdot(-1)+b\\\sf -a+b=3\\\sf f(3)=a\cdot3+b\\\sf 3a+b=1\\\begin{cases}\sf -a+b=3\\\sf 3a+b=1\end{cases}\\+\underline{\begin{cases}\sf -\diagdown\! \! \! \! 3a+3b=9\\\sf \diagdown\! \! \! \! 3a+b=1\end{cases}}\\\sf 4b=10\\\sf b=\dfrac{10\div2}{4\div2}=\dfrac{5}{2}\\\\\sf -a+b=3\\\sf a=b-3\\\sf a=\dfrac{5}{2}-3\\\\\sf a=\dfrac{5-6}{2}\\\\\sf a=-\dfrac{1}{2}\\\\\sf f(x) =-\dfrac{1}{2}x+\dfrac{5}{2}\\\\\sf f(1)=-\dfrac{1}{2}\cdot1+\dfrac{5}{2}\\\\\sf f(1)=-\dfrac{1}{2}+\dfrac{5}{2}\\\\\sf f(1)=\dfrac{4}{2}\\\\\sf f(1)=2\end{array}}$