Dada a função f(x)=ax + b , e sabendo- se que f(3) = 5 e f(-2) = -5.
Calcule f (
) .
Calcule f (
5.0
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a(3) + b = 5
3a + b = 5
II) f(-2) = - 5
a(-2) + b = - 5
- 2a + b = - 5
Fazendo um sistema de equações, temos:
{ 3a + b = 5
{- 2a + b = - 5 ×(-1)
{3a + b = 5
{2a - b = 5 +
5a + 0b = 10
5a = 10
a = 10
5
a = 2
3a + b = 5
3(2) + b = 5
6 + b = 5
b = 5 - 6
b = - 1
Formamos, então, a função.
f(x) = ax + b
f(x) = 2x - 1
Agora, calculamos o valor de f(1/2).
f(x) = 2x - 1
f(1/2) = 2(1/2) - 1
f(1/2) = 1 - 1
f(1/2) = 0
R.: 0