Question

Escreva a função afim f(x)=ax+b, sabendo que:

a)f(3)=4 e f(-1)=-12
b)f(7)=0 e f(-2)=9

Answer 1

[3 4 1]

[-1 -12 1] =0

[x. y. 1]

3[-12 1] -4 [-1 1] + 1[-1 -12] =0

[ y 1] [x 1] [x y ]

3(-12-y) -4(-1-x) +1(-y+12x) =0

-36-3y+4+4x-y+12x=0

16x-4y-32=0 (÷4)

4x-y-8=0

y= 4x-8 → f(x)=4x-8

b) [7 0 1]

[-2 9 1] =0

[x y 1]

7[9 1] +1 [-2 9] =0

[y 1] [x y]

7(9-y)+1(-2y-9x) =0

63-7y-2y-9x=0

-9x-9y+63=0 ÷(-9)

x+y-7=0

y=7-x→ f(x)=7-x