Question

v4) Sendo a função f ( x ) = ax + b com a, b ∈ e a 0, determine os valores de a e b de modo que f ( 3 ) = 4 e f ( - 1 ) = 2..

Answer 1

Resposta:

$a=\frac{1}{2}\\\\b=\frac{5}{2}$

Explicação passo a passo:

$f(x)=ax+b\\\\\\Para\ x=3\\\\4=3a+b\\\\Para\ x=-1\\\\2=-a+b\\\\\\Temos\ um\ sistema\ de\ equacoes.\\\\\left\{\begin{array}{ccc}3a+b=4\ (i)\\-a+b=2\ (ii)\end{array}\right\\\\\\3a=4-b\\\\a=\frac{4-b}{3}\ (iii)\\\\\\Substituindo\ o\ valor\ de\ (iii)\ em\ (ii):\\\\-(\frac{4-b}{3})+b=2\\\\\frac{-4+b}{3}+b=2\\\\3\bullet(\frac{-4+b}{3}+b)=3\bullet(2)\\\\-4+b+3b=6\\\\b+3b=6+4\\\\4b=10\\\\b=\frac{10}{4}\\\\b=\frac{5}{2}$

$Substituindo\ o\ valor\ de\ b\ em\ (iii):\\\\a=\frac{4-\frac{5}{2}}{3}\\\\a=\frac{\frac{8-5}{2}}{3}\\\\a=\frac{\frac{3}{2}}{3}\\\\a=(\frac{3}{2})\bullet(\frac{1}{3})\\\\a=\frac{3}{6}\\\\a=\frac{1}{2}$